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The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids. (English) Zbl 1477.06002

This paper studies the monoid structure of natural-valued monotone functions on an arbitrary poset is studied. A characterization of prime elements and a description of its convex hull are obtained. The associated monoid ring is proved to be normal, the Cohen-Macaulay type is determined, the Gorenstein property is characterized. These results are then applied to the monoid of quasi-arithmetic multiplicities on a uniform matroid.
Reviewer: Wei Yao (Nanjing)

MSC:

06A06 Partial orders, general
06A07 Combinatorics of partially ordered sets
05B35 Combinatorial aspects of matroids and geometric lattices
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