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