A generalization of MacMahon's formula
Mirjana Vuleti\'c
TL;DR
This paper extends MacMahon's formula for plane partitions and strict plane partitions using Macdonald's symmetric functions, providing new formulas and a bijective proof, especially simplified in the Hall-Littlewood case.
Contribution
It introduces a 2-parameter generalization of MacMahon's formulas related to Macdonald's symmetric functions and offers a bijective proof for strict plane partitions.
Findings
Generalized MacMahon's formula with two parameters
Simplified formula in the Hall-Littlewood case
Bijection proof for strict plane partitions
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Advanced Mathematical Identities