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

On the Class of Dominant and Subordinate Products

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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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