English

Lattice paths with given number of turns and semimodules over numerical semigroups

Combinatorics 2013-08-27 v4

Abstract

Let \Gamma=<\alpha, \beta > be a numerical semigroup. In this article we consider several relations between the so-called \Gamma-semimodules and lattice paths from (0,\alpha) to (\beta,0): we investigate isomorphism classes of \Gamma-semimodules as well as certain subsets of the set of gaps of \Gamma, and finally syzygies of \Gamma-semimodules. In particular we compute the number of \Gamma-semimodules which are isomorphic with their k-th syzygy for some k.

Keywords

Cite

@article{arxiv.1209.4797,
  title  = {Lattice paths with given number of turns and semimodules over numerical semigroups},
  author = {Julio José Moyano-Fernández and Jan Uliczka},
  journal= {arXiv preprint arXiv:1209.4797},
  year   = {2013}
}

Comments

15 pages. Extended version of our previous submission "Lattice paths with given number of turns and numerical semigroups"