On the Class of Dominant and Subordinate Products

Mathematics

Alexander Berkovich¹ 

关键词: q-series;    generating functions;    partition inequalities;    anti-telescoping;    rational functions with nonnegative coefficients;   

DOI  :  10.3390/math1020065

来源: mdpi

【 摘 要 】

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 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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.