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

Abstract

Let Γ =< α, ß> be a numerical semigroup. In this article we consider several relations between the so-called Γ -semimodules and lattice paths from (0, α) to (ß,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.