On Butler's unimodality result
type: Item
instance of: scholarly article
title: On Butler's unimodality result
zbMATH Open document ID: 0927.20036
DOI: 10.1007/PL00009832
author: Yugen Takegahara
published in: Combinatorica
publication date: 1999-09-14T00:00:00Z
review text: Let \(\lambda=(\lambda_i)_{i\in\omega}\) be a ``partition'', i.e., a decreasing sequence of non-negative integers \(\lambda_i\) which are 0 for almost all \(i\). Moreover let \(|\lambda|\) be the sum of these integers. Then \(\lambda\) can represent a finite abelian \(p\)-group \(A\) which is a direct sum of cyclic groups of order \(p^{\lambda_i}\), say \(A\) is of type \(\lambda\). If \(\alpha_\lambda(i,p)\) denotes the number of subgroups of \(A\) of order \(p^i\), then the author shows that the polynomial \(\alpha_\lambda(i,p)-\alpha_\lambda(i-1,p)\) in the variable \(p\) has non-negative coefficients. This was first shown by \textit{L. M. Butler} [Proc. Am. Math. Soc. 101, 771-775 (1987; Zbl 0647.20053)].
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1336360
zbMATH Keywords: Butler's unimodality result
zbMATH Keywords: finite Abelian \(p\)-groups
zbMATH Keywords: numbers of subgroups
MaRDI profile type: Publication
full work available at URL: pl00009832
OpenAlex ID: W2043025681
Recommended article: Proof of a conjecture on unimodality
Recommended article: On a Conjecture of Butler
Recommended article: Remarks on unimodularity
Recommended article: An extension of a criterion for unimodality
Recommended article: Unimodality problems in Ehrhart theory
Recommended article: On some results concerning univalence criteria
Recommended article: On a conjecture of Butler and Graham
Recommended article: Q5203127
Recommended article: Q3149636
Recommended article: The Odlyzko Conjecture and O'Hara's Unimodality Proof
description: scientific article; zbMATH DE number 1336360