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Mathematics 2013, 1(2), 65-75; doi:10.3390/math1020065
Article

On the Class of Dominant and Subordinate Products

*  and
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA
* Author to whom correspondence should be addressed.
Received: 25 March 2013 / Revised: 12 April 2013 / Accepted: 22 April 2013 / Published: 15 May 2013
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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.
Keywords: q-series; generating functions; partition inequalities; anti-telescoping; rational functions with nonnegative coefficients q-series; generating functions; partition inequalities; anti-telescoping; rational functions with nonnegative coefficients
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Berkovich, A.; Grizzell, K. On the Class of Dominant and Subordinate Products. Mathematics 2013, 1, 65-75.

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