Short generating functions for some semigroup algebras
type: Item
instance of: scholarly article
title: Short generating functions for some semigroup algebras
zbMATH Open document ID: 1023.05008
published in: The Electronic Journal of Combinatorics
publication date: 2003-09-24T00:00:00Z
full work available at URL: https://eudml.org/doc/122959
full work available at URL: v10i1r36.html
review text: Summary: Let \(a_1,\dots,a_n\) be distinct, positive integers with \((a_1,...,a_n)=1\), and let k be an arbitrary field. Let \(H(a_1,...,a_n;z)\) denote the Hilbert series of the graded algebra k\([t^{a_1},t^{a_2},...,t^{a_n}]\). We show that, when \(n=3\), this rational function has a simple expression in terms of \(a_1,a_2,a_3\); in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any \(n \geq 4\).
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 1985377
author: Graham Denham
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1985377