%0 Journal Article
%T On the Class of Dominant and Subordinate Products
%A Alexander Berkovich
%A Keith Grizzell
%J Mathematics
%D 2013
%I MDPI AG
%R 10.3390/math1020065
%X In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na¡§£¿ve 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.
%K q-series
%K generating functions
%K partition inequalities
%K anti-telescoping
%K rational functions with nonnegative coefficients
%U http://www.mdpi.com/2227-7390/1/2/65