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A generalization of MacMahon's formula · Around

2007

A generalization of MacMahon's formula

Vuletić, Mirjana

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We generalize the generating formula for plane partitions known as MacMahon's formula as well as its analog for strict plane partitions.

We give a 2-parameter generalization of these formulas related to Macdonald's symmetric functions.
The formula is especially simple in the Hall-Littlewood case.
We also give a bijective proof of the analog of MacMahon's formula for strict plane partitions.

Built on

P. N. Hoffman and J. F. Humphreys, Projective representations of the symmetric groups- Q-Functions and shifted tableaux
1992
Earlier work this paper cites.
I. G. Macdonald, Symmetric functions and Hall polynomials
1995
Earlier work this paper cites.

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R. Stanley, Enumerative combinatorics
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A. Okounkov and N. Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
2003
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M. Vuletić, Shifted Schur process and asymptotics of large random strict plane partitions
Original
Cited in the paper.

Then

A. Borodin and E. M. Rains, Eynard-Metha theorem, Schur process, and their Pffafian analogs
2005
Later among the works it cites.
O. Foda and M. Wheeler, BKP Plane Partitions
2007
Closest in time.

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