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Creators/Authors contains: "Torres_Davila, Eduardo"

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  1. ; ; (, The Electronic Journal of Combinatorics)
    This paper is the third in a series of manuscripts that examine the combinatorics of the Kunz polyhedron $$P_m$$, whose positive integer points are in bijection with numerical semigroups (cofinite subsemigroups of $$\mathbb Z_{\ge 0}$$) whose smallest positive element is $$m$$. The faces of $$P_m$$ are indexed by a family of finite posets (called Kunz posets) obtained from the divisibility posets of the numerical semigroups lying on a given face. In this paper, we characterize to what extent the minimal presentation of a numerical semigroup can be recovered from its Kunz poset. In doing so, we prove that all numerical semigroups lying on the interior of a given face of $$P_m$$ have identical minimal presentation cardinality, and we provide a combinatorial method of obtaining the dimension of a face from its corresponding Kunz poset. 
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