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

Show full item record

Page view(s)

1
Last Week
0
Last month
0
checked on Feb 26, 2024

Google ScholarTM

Check

Altmetric