McMahon's Formula via Free Fermions
John Mangual
TL;DR
This paper provides an elementary derivation of McMahon's formula for counting plane partitions using free fermions, clarifying previous complex derivations and introducing an interlacing operator.
Contribution
It offers a simplified, explicit derivation of McMahon's formula via free fermions, including new details and the definition of an interlacing operator.
Findings
Derivation of McMahon's formula using free fermions
Introduction of an interlacing operator for plane partitions
Clarification of previous complex derivations
Abstract
We give an elementary derivation of the vertex-operator derivation McMahon formula, counting all plane partitions of all size into a single generating function. We fill in some details appearing in Okounkov, Reshetikhin, and Vafa based on free fermions by defining an "interlacing operator".
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Markov Chains and Monte Carlo Methods