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Merge branch 'master' into mschauer-stirling
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‎.github/dependabot.yml‎

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# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
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version: 2
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updates:
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- package-ecosystem: "github-actions"
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directory: "/" # Location of package manifests
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schedule:
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interval: "weekly"

‎.github/workflows/CI.yml‎

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name: CI
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on:
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pull_request:
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push:
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branches:
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- master
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- main
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tags: '*'
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tags: ['*']
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pull_request:
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workflow_dispatch:
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concurrency:
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# Skip intermediate builds: always.
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# Cancel intermediate builds: only if it is a pull request build.
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group: ${{ github.workflow }}-${{ github.ref }}
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cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
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jobs:
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test:
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name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
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name: Julia ${{ matrix.version }} - ${{ matrix.os }}
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runs-on: ${{ matrix.os }}
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timeout-minutes: 60
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permissions: # needed to allow julia-actions/cache to proactively delete old caches that it has created
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actions: write
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contents: read
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strategy:
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fail-fast: false
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matrix:
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version:
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- '1.0'
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- '1.6'
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# - 'nightly'
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- '1.0' # compat
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- 'lts'
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- 'nightly'
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os:
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- ubuntu-latest
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- macOS-latest
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- macOS-latest # Apple silicon
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- windows-latest
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arch:
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- x64
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exclude:
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# Apple Silicon need julia >= v1.8
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- os: macos-latest
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version: '1.0'
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include:
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- os: macos-13 # Intel
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version: '1.0'
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@v1
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- uses: actions/checkout@v4
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- uses: julia-actions/setup-julia@v2
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with:
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version: ${{ matrix.version }}
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arch: ${{ matrix.arch }}
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- uses: actions/cache@v1
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env:
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cache-name: cache-artifacts
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with:
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path: ~/.julia/artifacts
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key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
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restore-keys: |
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${{ runner.os }}-test-${{ env.cache-name }}-
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${{ runner.os }}-test-
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${{ runner.os }}-
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- uses: julia-actions/cache@v2
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- uses: julia-actions/julia-buildpkg@v1
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- uses: julia-actions/julia-runtest@v1
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- uses: julia-actions/julia-processcoverage@v1
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- uses: codecov/codecov-action@v1
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- uses: codecov/codecov-action@v5
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with:
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token: ${{ secrets.CODECOV_TOKEN }} # required
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fail_ci_if_error: true
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files: lcov.info
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docs:
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name: Documentation
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runs-on: ubuntu-latest
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permissions:
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actions: write # needed to allow julia-actions/cache to proactively delete old caches that it has created
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contents: write
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statuses: write
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steps:
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- uses: actions/checkout@v4
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- uses: julia-actions/setup-julia@v2
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with:
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file: lcov.info
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version: '1'
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show-versioninfo: true
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- uses: julia-actions/cache@v2
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- name: Configure doc environment
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shell: julia --project=docs --color=yes {0}
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run: |
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using Pkg
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Pkg.develop(PackageSpec(path=pwd()))
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Pkg.instantiate()
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- uses: julia-actions/julia-buildpkg@v1
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- name: Run doctests
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shell: julia --project=docs --color=yes {0}
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run: |
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using Documenter: DocMeta, doctest
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using Combinatorics
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DocMeta.setdocmeta!(Combinatorics, :DocTestSetup, :(using Combinatorics); recursive=true)
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doctest(Combinatorics)
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- uses: julia-actions/julia-docdeploy@v1
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}

‎.github/workflows/CompatHelper.yml‎

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name: CompatHelper
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on:
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schedule:
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- cron: 0 0 * * *
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workflow_dispatch:
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jobs:
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CompatHelper:
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runs-on: ubuntu-latest
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steps:
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- name: Pkg.add("CompatHelper")
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run: julia -e 'using Pkg; Pkg.add("CompatHelper")'
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- name: CompatHelper.main()
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
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COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }}
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run: julia -e 'using CompatHelper; CompatHelper.main()'

‎.github/workflows/TagBot.yml‎

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name: TagBot
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on:
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schedule:
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- cron: 0 * * * *
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issue_comment:
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types:
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- created
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workflow_dispatch:
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inputs:
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lookback:
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default: 3
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# Workaround for https://github.com/JuliaRegistries/TagBot/issues/388
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# permissions:
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# actions: read
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# checks: read
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# contents: write
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# deployments: read
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# issues: read
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# discussions: read
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# packages: read
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# pages: read
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# pull-requests: read
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# repository-projects: read
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# security-events: read
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# statuses: read
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jobs:
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TagBot:
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if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
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runs-on: ubuntu-latest
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steps:
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- uses: JuliaRegistries/TagBot@v1
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with:
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token: ${{ secrets.GITHUB_TOKEN }}
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ssh: ${{ secrets.DOCUMENTER_KEY }}

‎.github/workflows/docsCI.yml‎

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‎Project.toml‎

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name = "Combinatorics"
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uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
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version = "1.0.2"
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version = "1.0.3"
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[compat]
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julia = "1"
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[extras]
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["LinearAlgebra", "Test"]
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test = ["LinearAlgebra", "OffsetArrays", "Test"]

‎README.md‎

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# Combinatorics
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[![Build Status](https://travis-ci.org/JuliaMath/Combinatorics.jl.svg?branch=master)](https://travis-ci.org/JuliaMath/Combinatorics.jl)
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](http://juliamath.github.io/Combinatorics.jl/)
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[![deps](https://juliahub.com/docs/General/Combinatorics/stable/deps.svg)](https://juliahub.com/ui/Packages/General/Combinatorics?t=2)
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[![CI](https://github.com/JuliaMath/Combinatorics.jl/actions/workflows/CI.yml/badge.svg)](https://github.com/JuliaMath/Combinatorics.jl/actions/workflows/CI.yml)
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[![Coverage Status](https://coveralls.io/repos/github/JuliaMath/Combinatorics.jl/badge.svg?branch=master)](https://coveralls.io/github/JuliaMath/Combinatorics.jl?branch=master)
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[![Codecov](https://codecov.io/gh/JuliaMath/Combinatorics.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaMath/Combinatorics.jl)
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[![codecov](https://codecov.io/gh/JuliaMath/Combinatorics.jl/graph/badge.svg?token=ov65P61lvZ)](https://codecov.io/gh/JuliaMath/Combinatorics.jl)
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A combinatorics library for Julia, focusing mostly (as of now) on enumerative
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combinatorics and permutations. As overflows are expected even for low values,

‎docs/src/README_old.md‎

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# Combinatorics
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[![Build Status](https://travis-ci.org/JuliaMath/Combinatorics.jl.svg?branch=master)](https://travis-ci.org/JuliaMath/Combinatorics.jl)
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[![CI](https://github.com/JuliaMath/Combinatorics.jl/actions/workflows/CI.yml/badge.svg)](https://github.com/JuliaMath/Combinatorics.jl/actions/workflows/CI.yml)
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[![Coverage Status](https://coveralls.io/repos/github/JuliaMath/Combinatorics.jl/badge.svg?branch=master)](https://coveralls.io/github/JuliaMath/Combinatorics.jl?branch=master)
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[![Codecov](https://codecov.io/gh/JuliaMath/Combinatorics.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaMath/Combinatorics.jl)
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[![codecov](https://codecov.io/gh/JuliaMath/Combinatorics.jl/graph/badge.svg?token=ov65P61lvZ)](https://codecov.io/gh/JuliaMath/Combinatorics.jl)
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A combinatorics library for Julia, focusing mostly (as of now) on enumerative
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combinatorics and permutations. As overflows are expected even for low values,

‎src/combinations.jl‎

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t::Int
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end
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function Base.iterate(c::Combinations, s = [min(c.t - 1, i) for i in 1:c.t])
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@inline function Base.iterate(c::Combinations, s = [min(c.t - 1, i) for i in 1:c.t])
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if c.t == 0 # special case to generate 1 result for t==0
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isempty(s) && return (s, [1])
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return
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Generate combinations of the elements of `a` of all orders. Chaining of order iterators
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is eager, but the sequence at each order is lazy.
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"""
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combinations(a) = Iterators.flatten([combinations(a, k) for k = 1:length(a)])
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combinations(a) = Iterators.flatten([combinations(a, k) for k = 0:length(a)])
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# cool-lex combinations iterator
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‎src/factorials.jl‎

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doublefactorial,
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hyperfactorial,
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multifactorial,
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gamma,
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primorial,
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multinomial
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end
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return f
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end
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function Base.factorial(n::BigInt, k::BigInt)
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if k < 0 || n < 0 || k > n
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throw(DomainError((n, k), "n and k must be nonnegative with k ≤ n"))
34+
end
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f = BigInt(1)
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n = deepcopy(n) # avoid mutating input
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while n > k
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Base.GMP.MPZ.mul!(f, n)
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Base.GMP.MPZ.sub_ui!(n, 1)
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end
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return f
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end
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Base.factorial(n::Integer, k::Integer) = factorial(promote(n, k)...)
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Compute the number of permutations of `n` with no fixed points, also known as the
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subfactorial. An alias `subfactorial` for this function is provided for convenience.
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"""
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function derangement(sn::Integer)
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n = BigInt(sn)
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return numerator(factorial(n) * sum([(-1)^k // factorial(k) for k = 0:n]))
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function derangement(n::Integer)
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if n < 0
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throw(DomainError(n, "n must be nonnegative"))
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elseif n <= 1
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return BigInt(1-n)
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end
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d = BigInt(0)
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for i in 2:n
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# d = i * d + (iseven(i) ? 1 : -1)
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Base.GMP.MPZ.mul_ui!(d, i)
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if iseven(i)
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Base.GMP.MPZ.add_ui!(d, 1)
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else
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Base.GMP.MPZ.sub_ui!(d, 1)
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end
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end
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return d
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end
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const subfactorial = derangement
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"""
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multinomial(k...)
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Multinomial coefficient where `n = sum(k)`.
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Compute the multinomial coefficient
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``\\binom{n}{k_1,k_2,...,k_i} = \\frac{n!}{k_1!k_2! \\cdots k_i!}, n = \\sum{k_i}``.
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Throws an `OverflowError` when the input is too large.
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See Also: `binomial`.
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# Examples
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```jldoctest
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julia> # (x+y)^2 = x^2 + 2xy + y^2
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julia> multinomial(2, 0)
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1
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julia> multinomial(1, 1)
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2
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julia> multinomial(0, 2)
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1
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julia> multinomial(10, 10, 10, 10)
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ERROR: OverflowError: 5550996791340 * 847660528 overflowed for type Int64
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Stacktrace:
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[...]
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```
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# External links
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- [Definitions](https://dlmf.nist.gov/26.4.2) on DLMF
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- [Multinomial theorem](https://en.wikipedia.org/wiki/Multinomial_theorem) on Wikipedia
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"""
100152
function multinomial(k...)
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s = 0
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result = 1
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@inbounds for i in k
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s += i
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result *= binomial(s, i)
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bi = binomial(s, i)
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result = Base.Checked.checked_mul(result, bi)
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end
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result
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end

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