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.