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.
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"