A triple product formula for plane partitions derived from biorthogonal polynomials

Shuhei Kamioka (1)

1 Department of Applied Mathematics and Physics [Kyoto]

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.

Domaines: Combinatoire [math.CO]

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⟩