Dyck paths and pattern-avoiding matchings

DOI10.1016/j.ejc.2005.07.013zbMath1106.05004arXivmath/0503327OpenAlexW1992104349MaRDI QIDQ854822

Vít Jelínek

Publication date: 7 December 2006

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503327

zbMATH Keywords

configurationcrossing edges

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (11)

On pattern avoidance in matchings and involutions ⋮ Counting with Borel's triangle ⋮ Patterns in ordered (random) matchings ⋮ The combinatorics of a tree-like functional equation for connected chord diagrams ⋮ A general theory of Wilf-equivalence for Catalan structures ⋮ Pattern avoidance in matchings and partitions ⋮ An infinite family of inv-Wilf-equivalent permutation pairs ⋮ Fillings of skew shapes avoiding diagonal patterns ⋮ \(k\)-noncrossing and \(k\)-nonnesting graphs and fillings of Ferrers diagrams ⋮ The combinatorics of associated Hermite polynomials ⋮ Enumeration of some classes of pattern avoiding matchings, with a glimpse into the matching pattern poset

Cites Work

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• Fixed points and excedances in restricted permutations
• A simple and unusual bijection for Dyck paths and its consequences
• A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths
• Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polyno\-mials
• Crossings and nestings of matchings and partitions

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