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On the Class of Dominant and Subordinate Products

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alexander Berkovich & Keith Grizzell, 2013. "On the Class of Dominant and Subordinate Products," Mathematics, MDPI, vol. 1(2), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:1:y:2013:i:2:p:65-75:d:25741
    as

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