We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements, and a description of its convex hull. We also study the associated monoid ring, proving that it is normal, and thus Cohen-Macaulay. We determine its Cohen-Macaulay type, characterize the Gorenstein property, and provide a Gröbner basis of the defining ideal. Then we apply these results to the monoid of quasi-arithmetic multiplicities on a uniform matroid. Finally we state some conjectures on the number of irreducibles for the monoid of multiplicities on an arbitrary matroid.

The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids / Bruns W.; Garcia-Sanchez P.A.; Moci L.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 569:(2021), pp. 377-400. [10.1016/j.jalgebra.2020.10.026]

The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids

Moci L.
2021

Abstract

We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements, and a description of its convex hull. We also study the associated monoid ring, proving that it is normal, and thus Cohen-Macaulay. We determine its Cohen-Macaulay type, characterize the Gorenstein property, and provide a Gröbner basis of the defining ideal. Then we apply these results to the monoid of quasi-arithmetic multiplicities on a uniform matroid. Finally we state some conjectures on the number of irreducibles for the monoid of multiplicities on an arbitrary matroid.
2021
The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids / Bruns W.; Garcia-Sanchez P.A.; Moci L.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 569:(2021), pp. 377-400. [10.1016/j.jalgebra.2020.10.026]
Bruns W.; Garcia-Sanchez P.A.; Moci L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/799535
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