A combinatorial interpretation of the \(p,q\)-hit numbers

DOI10.1016/j.disc.2007.11.028zbMath1189.05026OpenAlexW2140357470MaRDI QIDQ998346

Karen S. Briggs

Publication date: 28 January 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.11.028

zbMATH Keywords

hit numbersrook numbersFerrers boards\(p,q\)-analoguehit polynomial

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of representation theory (05E10)

Cites Work

• Rook theory and hypergeometric series
• Rook theory and cycle-counting permutation statistics
• \(p,q\)-Stirling numbers and set partition statistics
• 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
• Interpolating set partition statistics
• \(\sigma\)-restricted growth functions and \(p,q\)-Stirling numbers
• An interpretation for Garsia and Remmel's \(q\)-hit numbers
• Cycles and perfect matchings.
• Generalized rook polynomials
• Rook theory, generalized {S}tirling numbers and {\((p,q)\)}-analogues
• A \(p,q\)-analogue of a formula of Frobenius
• \(m\)-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
• The problem of the rooks and its applications
• Generalized Stirling Numbers, Convolution Formulae and p, q-Analogues
• Rook theory for perfect matchings

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