A Generalization of the q-Saalschütz Sum and the Burge Transform

  • Schilling A
  • Warnaar S
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Abstract

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.

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Schilling, A., & Warnaar, S. O. (2000). A Generalization of the q-Saalschütz Sum and the Burge Transform. In Physical Combinatorics (pp. 163–183). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-1378-9_5

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