Generalized rook polynomials

DOI10.1006/jcta.2000.3113zbMath0992.05009OpenAlexW2090969274MaRDI QIDQ1584670

James Haglund, Jay R. Goldman

Publication date: 11 September 2002

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

Full work available at URL: https://doi.org/10.1006/jcta.2000.3113

zbMATH Keywords

factorization theoremrook polynomialFerrers boardrook placement

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30)

Related Items

Weight-dependent commutation relations and combinatorial identities, Recent developments in combinatorial aspects of normal ordering, The drop polynomial of a weighted digraph, The commutation relation \(xy=qyx+hf(y)\) and Newton's binomial formula, Elliptic rook and file numbers, On the Stirling numbers associated with the meromorphic Weyl algebra, Some combinatorial arrays generated by context-free grammars, A combinatorial interpretation of the \(p,q\)-hit numbers, Elliptic extensions of the alpha-parameter model and the rook model for matchings, An elliptic extension of the general product formula for augmented rook boards, Unnamed Item, Rook-by-rook rook theory: Bijective proofs of rook and hit equivalences, File placements, fractional matchings, and normal ordering, Rook numbers and the normal ordering problem, Connection coefficients between generalized rising and falling factorial bases

Cites Work

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• Rook theory and hypergeometric series
• Bessel polynomials
• Q-counting rook configurations and a formula of Frobenius
• Rook theory. III: Rook polynomials and the chromatic structure of graphs
• Stirling polynomials
• \(q\)-rook polynomials and matrices over finite fields
• Rook placements and cellular decomposition of partition varieties
• An interpretation for Garsia and Remmel's \(q\)-hit numbers
• On the cover polynomial of a digraph
• A short proof of the rook reciprocity theorem
• The path-cycle symmetric function of a digraph
• The problem of the rooks and its applications
• Rook Theory. I.: Rook Equivalence of Ferrers Boards
• Rook Theory. II: Boards of Binomial Type
• Rook Theory-IV. Orthogonal Sequences of Rook Polynomials
• Proofs from THE BOOK
• Statistical problems involving permutations with restricted positions
• Generating Functions for Bessel and Related Polynomials