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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2020

A triple product formula for plane partitions derived from biorthogonal polynomials

Abstract

A new triple product formulae for plane partitions with bounded size of parts is derived from a combinato- rial interpretation of biorthogonal polynomials in terms of lattice paths. Biorthogonal polynomials which generalize the little q-Laguerre polynomials are introduced to derive a new triple product formula which recovers the classical generating function in a triple product by MacMahon and generalizes the trace-type generating functions in double products by Stanley and Gansner.
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Dates and versions

hal-02168179 , version 1 (28-06-2019)

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Shuhei Kamioka. A triple product formula for plane partitions derived from biorthogonal polynomials. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6333⟩. ⟨hal-02168179⟩
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