On the class of dominant and subordinate products
type: Item
instance of: scholarly article
title: On the class of dominant and subordinate products
zbMATH Open document ID: 1296.11131
author: Alexander Berkovich
author: Keith Grizzell
published in: Mathematics
publication date: 2014-08-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.2362
review text: Summary: In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a naïve version of \textit{G. E. Andrews}' anti-telescoping technique quite well [in: From Fourier analysis and number theory to Radon transforms and geometry. In Memory of Leon Ehrenpreis. Berlin: Springer. Developments in Mathematics 28, 1--20 (2013; Zbl 1318.11130)]. In addition, we prove (as a lemma to one of the theorems) a rather nontrivial class of rational functions of three variables has entirely nonnegative power series coefficients.
Mathematics Subject Classification ID: 11P82
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 11P84
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A20
zbMATH DE Number: 6334776
zbMATH Keywords: \(q\)-series
zbMATH Keywords: generating functions
zbMATH Keywords: partition inequalities
zbMATH Keywords: anti-telescoping
zbMATH Keywords: rational functions with nonnegative coefficients
MaRDI profile type: Publication
OpenAlex ID: W2093597384
arXiv ID: 1303.2362
cites work: Q4218535
cites work: Dissecting the Stanley partition function
cites work: Differences of Partition Functions: The Anti-telescoping Method
cites work: Races among products
cites work: A \(q\)-rious positivity
DOI: 10.3390/MATH1020065
description: scientific article; zbMATH DE number 6334776