An interpretation for Garsia and Remmel's \(q\)-hit numbers
Garsia and Remmel's \(q\)-analogue of the rook numbers and hit numbers associated with a Ferrers board is studied. A new recurrence for these \(q\)-hit numbers is found. Also, a statistic on permutations that constitutes a direct combinatorial interpretation of the \(q\)-hit numbers is defined. The statistic is used to prove a reciprocity theorem.
scientific article; zbMATH DE number 1123556