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A tableaux formula for $q$-rook numbers
Basu, Tirtharaj1; Bhattacharya, Aritra2
1The Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute, Chennai 600113, India
2Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 21-39

We provide a formula for the Garsia-Remmel $q$-rook numbers as a sum over standard Young tableaux. We connect our formula with the coefficients in $q$-Whittaker expansion of unicellular LLT functions.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.466
Classification: 05E05, 05A10, 05A30
Keywords: $q$-rook numbers, unicellular LLT functions, $q$-Whittaker functions, symmetric functions, Dyck paths

Basu, Tirtharaj  1 ; Bhattacharya, Aritra  2

1 The Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute, Chennai 600113, India
2 Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Basu, Tirtharaj; Bhattacharya, Aritra. A tableaux formula for $q$-rook numbers. Algebraic Combinatorics, Volume 9 (2026) no. 1, pp. 21-39. doi: 10.5802/alco.466

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