Merge pull request #83 from gap-packages/numerical-sets

Numerical sets

Author: ManuelAFDelgado

CHANGES

@@ -16,7 +16,25 @@
 - Added AsNumericalSemigroup for idemopotent ideals of numerical semigroups
 - Added IsStable for ideals of numerical semigroups
 - Improved DotBinaryRelation
-
+- Added numerical set category
+- Added conductor, multiplicity, gaps, small elements, Frobenius number for numerical sets
+- Print, string, display for numerical sets
+- Added membership for numerical sets
+- Added equality, inclusion and difference between numerical sets and numerical semigroups and ideals of numerical semigroups
+- Convert numerical semigroups to numerical sets and ideals of numerical semigroups to numerical sets (if the minimum element is zero)
+- Union, intersection and sum of numerical sets
+- Position and Positions for numerical sets
+- Added IsAssociatedNumericalSetOfNumericalSemigroup
+- Added AsNumericalSemigroup for numerical sets 
+- Added difference between numerical semigroups and ideals of numerical semigroups and vice versa
+- Added Position for ideals of numerical semigroups and numerical semigroups
+- Union of numerical semigroups is a numerical set
+- Integer partitions associated to numerical sets and numerical semigroups
+- Numerical sets associated to integer partitions
+- Hook lenghts associated to integer partitions of numerical sets and semigroups
+- Dual of a numerical set (and numerical semigroup)
+- Bonded, cojoint and end to end sum of numerical sets
+- Ferrers diagram of (the integer partition associated to a) numerical set or semigroup
 1.3.1 -> 1.4.0
 - Added NumericalSemigroupsWithFrobeniusNumberPC
 - Added NumericalSemigroupsWithGenusPC

PackageInfo.g

@@ -188,9 +188,18 @@ rec(
   IsAuthor      := false,
   IsMaintainer  := false,
   PostalAddress := "Universidad de Valladolid"
+),
+
+rec(
+  LastName      := "Yeşil",
+  FirstNames    := "Mehmet",
+  IsAuthor      := false,
+  IsMaintainer  := false,
+  PostalAddress := "Batman University"
 )
 
 
+
 ],
 
 Status := "accepted",

doc/Ideals_of_numerical_semigroups.xml

@@ -580,7 +580,8 @@ gap> MinimalGenerators(I+II);
                     <Description>
                         <A>I, J</A> are ideals of a numerical semigroup. <A>J</A> must be contained in <A>I</A>.
                         The output is the set <M><A>I</A>\setminus <A>J</A></M>.
-
+                        <P/>
+                        If one of the arguments is a numerical semigroup <M>S</M>, it is considered as the ideal <M>0+S</M>.
                         <Example><![CDATA[
 gap> S:=NumericalSemigroup(14, 15, 20, 21, 25);;
 gap> I:=[0,1]+S;

doc/NumericalSgps.bib

@@ -1644,3 +1644,24 @@ @article{ASICMNS
 year = {2024},
 doi = {10.1007/s00009-023-02550-8},
 }
+
+
+@article{Mehmet2025,
+	author = {Ye{\c s}il, Mehmet},
+	journal = {Results in Mathematics},
+	number = {7},
+	pages = {217},
+	title = {Young Diagram Decompositions for Almost Symmetric Numerical Semigroups},
+	volume = {80},
+	year = {2025}
+}
+
+@misc{kaplan2025,
+      title={On the smallest partition associated to a numerical semigroup}, 
+      author={Nathan Kaplan and Kaylee Kim and Cole McGeorge and Fabian Ramirez and Deepesh Singhal},
+      year={2025},
+      eprint={2507.04169},
+      archivePrefix={arXiv},
+      primaryClass={math.CO},
+      url={https://arxiv.org/abs/2507.04169}, 
+}

doc/NumericalSgps.fdb_latexmk

@@ -1,20 +1,20 @@
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+["bibtex NumericalSgps"] 1767943448.85139 "NumericalSgps.aux" "NumericalSgps.bbl" "NumericalSgps" 1767943448.91553 2
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+["pdflatex"] 1767943447.47401 "/Users/pedro/.gap/pkg/numericalsgps/doc/NumericalSgps.tex" "NumericalSgps.pdf" "NumericalSgps" 1767943448.91401 0
+  "/Users/pedro/.gap/pkg/numericalsgps/doc/NumericalSgps.tex" 1767901086.47631 629312 e91a7019e26329f7e7520b16c962e1c6 ""
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@@ -157,13 +157,13 @@
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