Rook-by-rook rook theory: Bijective proofs of rook and hit equivalences

DOI10.1016/j.aam.2008.09.003zbMath1169.05004OpenAlexW2006570242WikidataQ114214541 ScholiaQ114214541MaRDI QIDQ1015171

Nicholas A. Loehr, Jeffery B. Remmel

Publication date: 7 May 2009

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2008.09.003

zbMATH Keywords

\(q\)-analoguesinvolution principlehit equivalencerook equivalence

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30)

Related Items

Bijections on \(m\)-level rook placements, The combinatorics of Jeff Remmel

Cites Work

• Unnamed Item
• Unnamed Item
• \(p,q\)-Stirling numbers and set partition statistics
• Counting descent pairs with prescribed tops and bottoms
• Q-counting rook configurations and a formula of Frobenius
• A unified combinatorial approach for \(q\)- (and \(p,q\)-) Stirling numbers
• \(q\)-rook polynomials and matrices over finite fields
• An interpretation for Garsia and Remmel's \(q\)-hit numbers
• Generalized rook polynomials
• Rook theory, generalized {S}tirling numbers and {\((p,q)\)}-analogues
• A \(p,q\)-analogue of a formula of Frobenius
• Classifying descents according to parity
• \(m\)-rook numbers and a generalization of a formula of Frobenius to \(C_m \wr \mathcal S_n\)
• The q-Stirling numbers of first and second kinds
• Théorie géométrique des polynômes eulériens
• The problem of the rooks and its applications
• Method for constructing bijections for classical partition identities
• Rook Theory. I.: Rook Equivalence of Ferrers Boards
• Rook Theory. II: Boards of Binomial Type
• Rook theory for perfect matchings