On the Class of Dominant and Subordinate Products

Alexander Berkovich and Keith Grizzell
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Alexander Berkovich: Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA
Keith Grizzell: Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA

Mathematics, 2013, vol. 1, issue 2, 1-11

Abstract: 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.

Keywords: q-series; generating functions; partition inequalities; anti-telescoping; rational functions with nonnegative coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2013
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