A tableaux formula for $q$-rook numbers
Tirtharaj Basu, Aritra Bhattacharya
TL;DR
This paper introduces a tableaux-based formula for Garsia-Remmel $q$-rook numbers, linking combinatorial enumeration with symmetric function expansions.
Contribution
It presents a novel tableaux formula for $q$-rook numbers and connects it to $q$-Whittaker coefficients of LLT functions.
Findings
Derived a sum-over-tableaux formula for $q$-rook numbers
Established a connection with $q$-Whittaker expansion coefficients
Provides new combinatorial insights into symmetric functions
Abstract
We provide a formula for the Garsia-Remmel -rook numbers as a sum over standard Young tableaux. We connect our formula with the coefficients in -Whittaker expansion of unicellular LLT functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Random Matrices and Applications · Advanced Mathematical Identities