Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
A triple product formula for plane partitions derived from biorthogonal polynomials
Shuhei Kamioka  1  
1 : Department of Applied Mathematics and Physics [Kyoto]
Graduate School of Informatics Kyoto University 606-8501, Kyoto Japan -  Japon

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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