The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids
Autor(en): | Bruns, Winfried Garcia-Sanchez, Pedro A. Moci, Luca |
Stichwörter: | Affine monoid; Arithmetic matroid; Cohen-Macaulay type; Gorenstein property; INVARIANTS; Irreducible and prime elements; Mathematics; Monotone functions | Erscheinungsdatum: | 2021 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | JOURNAL OF ALGEBRA | Volumen: | 569 | Startseite: | 377 | Seitenende: | 400 | Zusammenfassung: | 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 Grobner 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. (C) 2020 Elsevier Inc. All rights reserved. |
ISSN: | 00218693 | DOI: | 10.1016/j.jalgebra.2020.10.026 |
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geprüft am 15.05.2024