diff --git a/src/math/rs_algorithm.jl b/src/math/rs_algorithm.jl
new file mode 100644
index 00000000..7541f611
--- /dev/null
+++ b/src/math/rs_algorithm.jl
@@ -0,0 +1,1443 @@
+### A Pluto.jl notebook ###
+# v0.19.32
+
+using Markdown
+using InteractiveUtils
+
+# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
+macro bind(def, element)
+ quote
+ local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
+ local el = $(esc(element))
+ global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
+ el
+ end
+end
+
+# ╔═╡ 087084fe-a3d8-4ef5-8819-22787e885844
+using Random
+
+# ╔═╡ e76fa719-b8a2-4a3d-bf29-bbac6b64808b
+using Plots, PlutoUI
+
+# ╔═╡ 4db253c8-6c3c-11ee-2921-45f9793427aa
+using YoungTableaux
+
+# ╔═╡ 50401b76-6c95-48c9-8ce6-a96281e911ff
+using HypertextLiteral, AbstractPlutoDingetjes.Bonds
+
+# ╔═╡ 322aec90-7ec6-4131-8625-bbd32afbe0b1
+using UUIDs
+
+# ╔═╡ 7b3aadec-4ec4-4f89-8ccb-c78c24bad000
+md"""
+# The RS algorithm visualized
+
+Try plugging in your own name:
+"""
+
+# ╔═╡ ef2fac57-ff72-400a-bc18-2e4eadafac11
+begin
+ s = collect("PLUTOROCKS");
+ Text(String(s))
+end
+
+# ╔═╡ b4fcb4ce-5474-49e5-81c6-0cf6a2024643
+@htl """
+Show Record $(@bind show_Q CheckBox())
+"""
+
+# ╔═╡ 0acd1cda-9a65-4730-a451-6369dfbb92f8
+function schensted_insert!(rows, k, i=1)
+ i > length(rows) && return push!(rows, [k]), i
+ row = rows[i]
+ for (j, m) in pairs(row)
+ k < m || continue
+ row[j] = k
+ return schensted_insert!(rows, m, i+1)
+ end
+ push!(row, k)
+ return rows, i
+end
+
+# ╔═╡ 47e58152-f784-40e6-9616-eb7d31fa606c
+function rs_pair(j)
+ T = eltype(j)
+ P, Q = Vector{eltype(j)}[], Vector{Int}[]
+ for (n, k) in enumerate(j)
+ P, i = schensted_insert!(P, k)
+ # record index for j in Q in the same row i
+ Q, _i = schensted_insert!(Q, n, i)
+ @assert i == _i
+ end
+ return YoungTableau(P), YoungTableau(Q)
+end
+
+# ╔═╡ a8ca7dae-72e6-4ff8-9171-8a22c48f0e49
+md"""
+What happens if we plug in a permutation of the numbers from ``1`` through ``N`` instead?
+"""
+
+# ╔═╡ 61851b37-4fdf-4702-82ab-9fdca6cf42d2
+π = randperm(16)
+
+# ╔═╡ 37dc5a55-8dc7-4dfa-854b-2463bc1863bc
+md"""
+Logan-Shepp limit shape on [-2,2] when rotated 45 degrees
+``\frac{2}{\pi}(x*\arcsin(x)/2 + \sqrt{4-x^2} )``
+
+**Reference:**
+
+Borodin, A., Okounkov, A., & Olshanski, G. (2000). Asymptotics of Plancherel measures for symmetric groups. Journal of the American Mathematical Society, 13(3), 481-515.
+Equation for ``\Omega(u)`` at the bottom of page 2
+"""
+
+# ╔═╡ 2626db42-96cb-49c6-ab26-8053fa7fab66
+x = [1,3,3,2,2,1,2]
+
+# ╔═╡ 74b9394b-c57b-4d47-ac2e-0925cb46fac1
+rs_pair(x)
+
+# ╔═╡ f9536da7-8743-43d2-a9b8-b432ead8c99d
+md"""
+Recreation of [https://math.mit.edu/events/stanley70/savethedate/]():
+"""
+
+# ╔═╡ 877b720b-b96d-4316-b0d2-8cb65aef6304
+name = uppercase("richardpstanley")
+
+# ╔═╡ 65cbdc74-cec1-48cd-ae6a-a0cd5fca424e
+P, Q = rs_pair(name)
+
+# ╔═╡ 4e1a8c4a-b7bd-4e4d-a3ba-5b9493bfe769
+('A':'Z')[Q]
+
+# ╔═╡ f78d304e-9bc6-41cd-8cd4-62b88215ff19
+begin
+ log!(::Nothing, _...) = nothing
+ log!(x, rows, (i, j), k) = push!(x, (YoungTableau(copy.(rows)), (i, j), k))
+ sublog!(::Nothing) = nothing
+ sublog!(x) = (y = Any[]; push!(x, y); y)
+end
+
+# ╔═╡ 0f6bc3dd-505b-4000-80db-fa17d39ee47a
+function _schensted_insert!(rows, k, i=1; log=nothing)
+ if i > length(rows)
+ log!(log, rows, (i, 1), k)
+ return push!(rows, [k]), i
+ end
+ row = rows[i]
+ for (j, m) in pairs(row)
+ k < m || continue
+ log!(log, rows, (i, j), k)
+ row[j] = k
+ return _schensted_insert!(rows, m, i+1; log)
+ end
+ log!(log, rows, (i, lastindex(row)+1), k)
+ push!(row, k)
+ return rows, i
+end
+
+# ╔═╡ 20df36ae-9191-4700-b963-7f80cec971d8
+function _rs_pair(j; log_P=nothing, log_Q=nothing)
+ T = eltype(j)
+ P, Q = Vector{eltype(j)}[], Vector{Int}[]
+ for (n, k) in enumerate(j)
+ P, i = _schensted_insert!(P, k; log=sublog!(log_P))
+ Q, _i = _schensted_insert!(Q, n, i; log=sublog!(log_Q))
+ @assert i == _i
+ end
+ return YoungTableau(P), YoungTableau(Q)
+end
+
+# ╔═╡ d29210b7-f3fd-4a66-997a-9f19373290ec
+function calc_steps(s)
+ _STEPS_P, _STEPS_Q = Any[], Any[]
+ _rs_pair(s; log_P=_STEPS_P, log_Q=_STEPS_Q)
+ return (
+ [(idx, x, i == lastindex(y)) for (idx, y) in enumerate(_STEPS_P) for (i, x) in enumerate(y)],
+ [x for (idx, y) in enumerate(_STEPS_Q) for x in y],
+ )
+end
+
+# ╔═╡ 358b2401-9c0b-43aa-816a-7312db17f677
+STEPS_P_Π, STEPS_Q_Π = calc_steps(π);
+
+# ╔═╡ e455823e-62df-4b0d-a145-584d54557353
+STEPS_P, STEPS_Q = calc_steps(s);
+
+# ╔═╡ 9c7803cf-cf92-4573-a6b8-d88e51b5919e
+function visualize_insert((yt, to_replace, x); delete=true)
+ YoungTableaux.visualize_insert(yt, x, to_replace[1]; to_replace, delete)
+end
+
+# ╔═╡ 8e43cf19-0a50-486d-8220-3372ff41801f
+function visualize_step(STEP_P, s, STEPS_Q=nothing; show_Q=false)
+ idx = STEP_P[1]
+ @htl """
+
+
+ $(visualize_insert(STEP_P[2]))
+ $(if show_Q
+ visualize_insert(Base.setindex(STEPS_Q[idx], (STEP_P[2][2][1], STEP_P[3] ? STEPS_Q[idx][2][2] : 0), 2); delete=STEP_P[3])
+ end)
+
+
+ $(YoungTableau([collect(Iterators.flatten((' '^idx, s[idx+1:end])))]))
+ """
+end
+
+# ╔═╡ ed00d350-b394-4db9-ad7a-c0a9db65b6a6
+begin
+ struct SeekingSlider
+ r::StepRange{Int, Int}
+ default::Int
+ end
+ function Base.show(io::IO, ::MIME"text/html", (; r, default)::SeekingSlider)
+ print(io, @htl("""
+
+
+
+
+
+
+ $default
+
+
+
+ """))
+ end
+ Base.get((; default)::SeekingSlider) = default
+ Bonds.initial_value((; default)::SeekingSlider) = default
+ Bonds.possible_values((; r)::SeekingSlider) = r
+end
+
+# ╔═╡ 9f1c4744-b629-4bf8-b8b2-caf812efc496
+@bind i SeekingSlider(eachindex(STEPS_P), 1)
+
+# ╔═╡ e3c074b4-7d4e-4a02-8d14-ffdc54439ecb
+visualize_step(STEPS_P[i], s, STEPS_Q; show_Q)
+
+# ╔═╡ 7d3f7f83-5af3-4d4b-8299-2f429d026622
+@bind i_π SeekingSlider(eachindex(STEPS_P_Π), 1)
+
+# ╔═╡ 9bc40166-338b-4060-bb76-16e30e3f7086
+visualize_step(STEPS_P_Π[i_π], π, STEPS_Q_Π; show_Q)
+
+# ╔═╡ 3abc835b-2f8a-4553-92c2-41e47b3e32f4
+@bind N SeekingSlider(0:20:700, 0)
+
+# ╔═╡ 200c88f2-159a-4693-bee8-e3ccc271d781
+begin
+ Z, _ = rs_pair(randperm(N))
+ X = [j for i in 1:nrows(Z) for j in 1:length(row(Z, i))]
+ Y = [i for i in 1:nrows(Z) for j in 1:length(row(Z, i))]
+ # Logan-Shepp Limit
+ # -2 <= u <- 2
+ Ω(u) = [abs(ℓ/2) > 1 ? abs(ℓ) : 2/pi*(ℓ * asin(ℓ/2) + sqrt(4-ℓ^2)) for ℓ ∈ u ]
+ u = (X - Y)/sqrt(N)#scale by cardinality of partition
+ v = (X + Y)/sqrt(N)
+ p1 = scatter(u,v,markershape=:circle,markersize=:100/sqrt(N),
+ markercolor = :white,
+ markerstrokewidth = 0.5,legend=false)
+ plot!(ℓ->2/pi*(ℓ * asin(ℓ/2) + sqrt(4-ℓ^2)) ,-2,2,linewidth=:3,ylims=(0,2.5),xlims=(-2.5,2.5),ratio=1,color=:red)
+ #plot!(p1, sort(u), Ω(sort(u)),linewidth=:5,ylims=(0,2.5),xlims=(-2.5,2.5),ratio=1)
+end
+
+# ╔═╡ 01059a74-a4e4-4962-8515-a8a333176a15
+function small_yt(yt)
+ class_yt = string("yt-", uuid1())
+ @htl """
+
+ $(HTML(repr("text/html", yt; context=:html_class => class_yt)))
+ """
+end
+
+# ╔═╡ c0b78cdc-5702-44c4-8989-ab86587daa2b
+small_yt(Z)
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+AbstractPlutoDingetjes = "6e696c72-6542-2067-7265-42206c756150"
+HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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+YoungTableaux = "b7062236-b0aa-4473-bf76-66f344053691"
+
+[compat]
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+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.9.4"
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+version = "1.2.13+0"
+
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.5+0"
+
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.43.0+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
+
+[[deps.libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.8.0+0"
+
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[deps.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "f7c281e9c61905521993a987d38b5ab1d4b53bef"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+1"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.52.0+1"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+version = "17.4.0+0"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+1"
+"""
+
+# ╔═╡ Cell order:
+# ╟─7b3aadec-4ec4-4f89-8ccb-c78c24bad000
+# ╠═ef2fac57-ff72-400a-bc18-2e4eadafac11
+# ╟─9f1c4744-b629-4bf8-b8b2-caf812efc496
+# ╟─b4fcb4ce-5474-49e5-81c6-0cf6a2024643
+# ╠═e3c074b4-7d4e-4a02-8d14-ffdc54439ecb
+# ╠═0acd1cda-9a65-4730-a451-6369dfbb92f8
+# ╠═47e58152-f784-40e6-9616-eb7d31fa606c
+# ╟─a8ca7dae-72e6-4ff8-9171-8a22c48f0e49
+# ╠═087084fe-a3d8-4ef5-8819-22787e885844
+# ╠═61851b37-4fdf-4702-82ab-9fdca6cf42d2
+# ╠═358b2401-9c0b-43aa-816a-7312db17f677
+# ╟─7d3f7f83-5af3-4d4b-8299-2f429d026622
+# ╠═9bc40166-338b-4060-bb76-16e30e3f7086
+# ╠═e76fa719-b8a2-4a3d-bf29-bbac6b64808b
+# ╠═3abc835b-2f8a-4553-92c2-41e47b3e32f4
+# ╠═200c88f2-159a-4693-bee8-e3ccc271d781
+# ╟─37dc5a55-8dc7-4dfa-854b-2463bc1863bc
+# ╠═c0b78cdc-5702-44c4-8989-ab86587daa2b
+# ╠═2626db42-96cb-49c6-ab26-8053fa7fab66
+# ╠═74b9394b-c57b-4d47-ac2e-0925cb46fac1
+# ╟─f9536da7-8743-43d2-a9b8-b432ead8c99d
+# ╠═877b720b-b96d-4316-b0d2-8cb65aef6304
+# ╠═65cbdc74-cec1-48cd-ae6a-a0cd5fca424e
+# ╠═4e1a8c4a-b7bd-4e4d-a3ba-5b9493bfe769
+# ╠═f78d304e-9bc6-41cd-8cd4-62b88215ff19
+# ╠═0f6bc3dd-505b-4000-80db-fa17d39ee47a
+# ╠═20df36ae-9191-4700-b963-7f80cec971d8
+# ╠═d29210b7-f3fd-4a66-997a-9f19373290ec
+# ╠═e455823e-62df-4b0d-a145-584d54557353
+# ╠═9c7803cf-cf92-4573-a6b8-d88e51b5919e
+# ╠═8e43cf19-0a50-486d-8220-3372ff41801f
+# ╠═4db253c8-6c3c-11ee-2921-45f9793427aa
+# ╠═50401b76-6c95-48c9-8ce6-a96281e911ff
+# ╠═ed00d350-b394-4db9-ad7a-c0a9db65b6a6
+# ╠═322aec90-7ec6-4131-8625-bbd32afbe0b1
+# ╠═01059a74-a4e4-4962-8515-a8a333176a15
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002