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Hypergeometric Identities Associated with Statistics on Words

In: Advances in Combinatorics

Author

Listed:
  • George E. Andrews

    (The Pennsylvania State University, Department of Mathematics)

  • Carla D. Savage

    (North Carolina State University, Department of Computer Science)

  • Herbert S. Wilf

    (University of Pennsylvania, Department of Mathematics)

Abstract

We show how combinatorial arguments involving a variety of statistics on words can produce nontrivial identities between hypergeometric series in two variables. We establish relationships to the Rogers-Fine identity, Heine’s second transformation, and mock theta functions. Finally, we show that any hypergeometric series of a certain form can be interpreted in terms of generalized statistics on words.

Suggested Citation

  • George E. Andrews & Carla D. Savage & Herbert S. Wilf, 2013. "Hypergeometric Identities Associated with Statistics on Words," Springer Books, in: Ilias S. Kotsireas & Eugene V. Zima (ed.), Advances in Combinatorics, edition 127, pages 77-100, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-30979-3_4
    DOI: 10.1007/978-3-642-30979-3_4
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