English

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