Crossings over permutations avoiding some pairs of patterns of length three

zbMath1442.05009arXiv1910.13809MaRDI QIDQ5113816

Arthur Randrianarivony, Sandrataniaina R. Andriantsoa, Paul M. Rakotomamonjy

Publication date: 17 June 2020

Full work available at URL: https://arxiv.org/abs/1910.13809

zbMATH Keywords

generating functioncombinatorial interpretationcrossingstatisticexpected pattern

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05)

Related Items (1)

Crossings and nestings over some Motzkin objects and \(q\)-Motzkin numbers

Uses Software

• OEIS
• AARON

Cites Work

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• Crossings of signed permutations and \(q\)-Eulerian numbers of type \(B\)
• Permutation patterns and statistics
• Bijections for refined restricted permutations
• Restricted permutations refined by number of crossings and nestings
• \(q,p\)-Catalan numbers
• Refined restricted permutations
• Multiple pattern avoidance with respect to fixed points and excedances
• Crossings and alignments of permutations
• Total occurrence statistics on restricted permutations
• On k-crossings and k-nestings of permutations
• Distributions of Statistics over Pattern-Avoiding Permutations
• Restricted permutations
• Continued fractions, \(q\)-Catalan numbers, and \(q\)-Genocchi polynomials

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