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March 5, 2026Algebraic Combinatorics0 citationsOpen Access

A tableaux formula for q -rook numbers

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TBTirtharaj BasuABAritra Bhattacharya

Key Points

  • The objective is to provide a formula for Garsia-Remmel Q-rook numbers and explore its connections.
  • Developed a formula based on standard Young tableaux.
  • Analyzed coefficients in the Q-Whittaker expansion of unicellular LLT functions.
  • Introduced a new sum representation for Q-rook numbers.
  • Established links between the formula and existing mathematical structures.

Abstract

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.

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Cite This Study

Basu et al. (2026) studied this question.

synapsesocial.com/papers/69a91db5d6127c7a504c0c86https://doi.org/10.5802/alco.466
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