Elliptic rook and file numbers
Copyright policy )Elliptic rook and file numbers
In this work, we construct elliptic analogues of the rook numbers and file numbers by attaching elliptic weights to the cells in a board. We show that our elliptic rook and file numbers satisfy elliptic extensions of corre- sponding factorization theorems which in the classical case were established by Goldman, Joichi and White and by Garsia and Remmel in the file number case. This factorization theorem can be used to define elliptic analogues of various kinds of Stirling numbers of the first and second kind as well as Abel numbers. We also give analogous results for matchings of graphs, elliptically extending the result of Haglund and Remmel.
- University of Vienna Austria
- Simon Fraser University Canada
- Sungkyunkwan University Korea (Republic of)
\(q\)-analogues, Exact enumeration problems, generating functions, 05A19 (Primary) 05A15, 05A30, 11B65, 11B73, 11B83 (Secondary), Trees, Stirling numbers, Lah numbers, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], QA1-939, FOS: Mathematics, Mathematics - Combinatorics, 101012 Kombinatorik, Combinatorial identities, bijective combinatorics, file numbers, 101012 Combinatorics, [math.math-co]mathematics [math]/combinatorics [math.co], combinatorial identities, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Combinatorics, combinatorics, \(q\)-calculus and related topics, Combinatorics (math.CO), elliptic analogues, Mathematics, rook numbers
\(q\)-analogues, Exact enumeration problems, generating functions, 05A19 (Primary) 05A15, 05A30, 11B65, 11B73, 11B83 (Secondary), Trees, Stirling numbers, Lah numbers, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], QA1-939, FOS: Mathematics, Mathematics - Combinatorics, 101012 Kombinatorik, Combinatorial identities, bijective combinatorics, file numbers, 101012 Combinatorics, [math.math-co]mathematics [math]/combinatorics [math.co], combinatorial identities, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Combinatorics, combinatorics, \(q\)-calculus and related topics, Combinatorics (math.CO), elliptic analogues, Mathematics, rook numbers
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