An interpretation for Garsia and Remmel's \(q\)-hit numbers

DOI10.1006/jcta.1997.2823zbMath0891.05008OpenAlexW2001240420MaRDI QIDQ1380346

Morris Dworkin

Publication date: 4 March 1998

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.1997.2823

zbMATH Keywords

reciprocity theorem\(q\)-analoguehit numbersrook numbersstatisticFerrers board

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30)

Related Items

Bijections on \(m\)-level rook placements ⋮ Atomic-AES: A Compact Implementation of the AES Encryption/Decryption Core ⋮ Remixed Eulerian numbers ⋮ Random oracle combiners: breaking the concatenation barrier for collision-resistance ⋮ Chromatic symmetric functions from the modular law ⋮ A cornucopia of quasi-Yamanouchi tableaux ⋮ Eulerian polynomials via the Weyl algebra action ⋮ Elliptic rook and file numbers ⋮ Rook theory and cycle-counting permutation statistics ⋮ \(m\)-rook numbers and a generalization of a formula of Frobenius to \(C_m \wr \mathcal S_n\) ⋮ Rook theory for perfect matchings ⋮ A combinatorial interpretation of the \(p,q\)-hit numbers ⋮ Elliptic extensions of the alpha-parameter model and the rook model for matchings ⋮ Chromatic symmetric functions of Dyck paths and \(q\)-rook theory ⋮ Chromatic symmetric functions of Dyck paths and \(q\)-rook theory ⋮ Rook-by-rook rook theory: Bijective proofs of rook and hit equivalences ⋮ Generalized rook polynomials ⋮ Rook Theory of the Finite General Linear Group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Q-counting rook configurations and a formula of Frobenius
• On the cover polynomial of a digraph
• The path-cycle symmetric function of a digraph
• Recursive statistics on words
• A Combinatorial Property of q-Eulerian Numbers
• Rook Theory. I.: Rook Equivalence of Ferrers Boards