On the class of dominant and subordinate products
Number Theory
2013-03-12 v1 Combinatorics
Abstract
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na\"ive version of Andrews' anti-telescoping technique quite well. These new theorems also put to rest any notion that including parts of size 1 is somehow necessary in order to have a valid irreducible partition inequality. 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.
Keywords
Cite
@article{arxiv.1303.2362,
title = {On the class of dominant and subordinate products},
author = {Alexander Berkovich and Keith Grizzell},
journal= {arXiv preprint arXiv:1303.2362},
year = {2013}
}
Comments
10 pages