2012/09/21 by Julio José Moyano‐Fernández, Julio José Moyano-Fernández, Moyano-Fernández, Julio José +2
Computer Science · Mathematics · #05A19 #20M14 #Advanced Algebra and Logic #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Rings, Modules, and Algebras #math.CO #msc:05A19 #msc:20M14
paper · pdf · doi:10.48550/arxiv.1209.4797
15 pages. Extended version of our previous submission "Lattice paths with given number of turns and numerical semigroups"
openalex publication_date 2012/09/21 · arxiv created 2013/08/26 · arxiv updated 2013/08/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Let Γ=<α, β> be a numerical semigroup. In this article we consider several relations between the so-called Γ-semimodules and lattice paths from (0,α) to (β,0): we investigate isomorphism classes of Γ-semimodules as well as certain subsets of the set of gaps of Γ, and finally syzygies of Γ-semimodules. In particular we compute the number of Γ-semimodules which are isomorphic with their k-th syzygy for some k.