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On the Class of Dominant and Subordinate Products

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Author(s): Alexander Berkovich | Keith Grizzell

Journal: Mathematics
ISSN 2227-7390

Volume: 1;
Issue: 2;
Start page: 65;
Date: 2013;
Original page

Keywords: q-series | generating functions | partition inequalities | anti-telescoping | rational functions with nonnegative coefficients

ABSTRACT
In this paper we provide proofs of two new theorems that provide a broad class of partition inequalities and that illustrate a na¨ıve 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.
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