A tableaux formula for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -rook numbers
We provide a formula for the Garsia-Remmel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -rook numbers as a sum over standard Young tableaux. We connect our formula with the coefficients in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -Whittaker expansion of unicellular LLT functions.
Authors
- Tirtharaj Basu
- Aritra Bhattacharya (ORCID: https://orcid.org/0000-0001-7140-6823)
Institutions
- Homi Bhabha National Institute (IN)
- Peking University (CN)
- Peking University International Hospital (CN)
- Institute of Mathematical Sciences (IN)
Publication Details
- Journal
- Algebraic Combinatorics
- Published
- 2026-03-03
- DOI
- https://doi.org/10.5802/alco.466
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00