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Equidistributed Statistics on Matchings and Permutations
Örebro University, School of Science and Technology, Örebro University, Sweden.ORCID iD: 0000-0002-6444-7878
Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden.
2014 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 21, no 4, P4.43Article in journal (Refereed) Published
Abstract [en]

We show that the bistatistic of right nestings and right crossings in matchings without left nestings is equidistributed with the number of occurrences of two certain patterns in permutations, and furthermore that this equidistribution holds when refined to positions of these statistics in matchings and permutations. For this distribution we obtain a non-commutative generating function which specializes to Zagier's generating function for the Fishburn numbers after abelianization. As a special case we obtain proofs of two conjectures of Claesson and Linusson. Finally, we conjecture that our results can be generalized to involving left crossings of matchings too.

Place, publisher, year, edition, pages
Electronic Journal of Combinatorics , 2014. Vol. 21, no 4, P4.43
Keyword [en]
permutation, pattern, matching, nesting, crossing
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-39040ISI: 000363516600004Scopus ID: 2-s2.0-84912122653OAI: oai:DiVA.org:oru-39040DiVA: diva2:766418
Funder
Swedish Research Council, 621-2009-6090
Available from: 2014-11-27 Created: 2014-11-27 Last updated: 2015-11-16Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
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