2018/03/19 by Pedro A. García-Sánchez, García-Sánchez, P. A., D. Marín-Aragón +3
Computer Science · Mathematics · #20M14 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1803.06879
openalex publication_date 2018/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the number of numerical semigroups with multiplicity three, four or five and fixed genus is increasing as a function in the genus. To this end we use the Kunz polytope for these multiplicities. Counting numerical semigroups with fixed multiplicity and genus is then an integer partition problem with some extra conditions (those of membership to the Kunz polytope). For the particular case of multiplicity four, we are able to prove that the number of numerical semigroups with multiplicity four and genus g is the number of partitions x+y+z=g+6 with 0