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Equidistributed Statistics on Matchings and Permutations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
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
The Electronic Journal of Combinatorics , 2014. Vol. 21, no 4, P4.43
Keyword [en]
Permutation, Pattern, Matching, Nesting, Crossing
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-177001ISI: 000363516600004Scopus ID: 2-s2.0-84912122653OAI: oai:DiVA.org:kth-177001DiVA: diva2:871525
Funder
Swedish Research Council, 621-2009-6090
Note

QC 20151116

Available from: 2015-11-16 Created: 2015-11-13 Last updated: 2017-12-01Bibliographically approved

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