$n!$ matchings, $n!$ posets

DOI10.1090/S0002-9939-2010-10678-0zbMath1237.05004arXiv1003.4728WikidataQ60692424 ScholiaQ60692424MaRDI QIDQ3082312

Anders Claesson, Svante Linusson

Publication date: 10 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4728

zbMATH Keywords

pattern avoiding permutations(2+2)-free posetsfactorial posetsmatching without neighbor nestings

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05)

Related Items (18)

Proof of a bi-symmetric septuple equidistribution on ascent sequences ⋮ Asymptotics and statistics on Fishburn matrices: Dimension distribution and a conjecture of Stoimenow ⋮ Fishburn trees ⋮ Bi-symmetric multiple equidistributions on ascent sequences ⋮ The history of the Gothenburg--Reykjavík--Strathclyde combinatorics group ⋮ Partitions and partial matchings avoiding neighbor patterns ⋮ Symmetric generating functions and Euler-Stirling statistics on permutations ⋮ Counting general and self-dual interval orders ⋮ Asymptotics and statistics on Fishburn matrices and their generalizations ⋮ Equidistributed statistics on matchings and permutations ⋮ Equidistributed statistics on Fishburn matrices and permutations ⋮ Catalan pairs and Fishburn triples ⋮ Partition and composition matrices ⋮ Ascent sequences avoiding pairs of patterns ⋮ A new decomposition of ascent sequences and Euler-Stirling statistics ⋮ Hereditary semiorders and enumeration of semiorders by dimension ⋮ An operator on ascent sequences ⋮ Weak ascent sequences and related combinatorial structures

Uses Software

• OEIS

Cites Work

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• An obvious proof of Fishburn's interval order theorem
• The Cauchy identity for \(Sp(2n)\)
• Ascent sequences and upper triangular matrices containing non-negative integers
• (2+2)-free posets, ascent sequences and pattern avoiding permutations
• Interval graphs and interval orders
• Distribution of crossings, nestings and alignments of two edges in matchings and partitions
• Intransitive indifference with unequal indifference intervals
• On the Enumeration of Decision Patterns Involving $n$ Means
• ENUMERATION OF CHORD DIAGRAMS AND AN UPPER BOUND FOR VASSILIEV INVARIANTS
• Intransitive Indifference in Preference Theory: A Survey
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

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