Change search
ReferencesLink to record
Permanent link

Direct link
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
URN: urn:nbn:se:kth:diva-177001ISI: 000363516600004ScopusID: 2-s2.0-84912122653OAI: diva2:871525
Swedish Research Council, 621-2009-6090

QC 20151116

Available from: 2015-11-16 Created: 2015-11-13 Last updated: 2015-11-18Bibliographically approved

Open Access in DiVA

No full text

Other links

ScopusPublished version

Search in DiVA

By author/editor
Sjöstrand, Jonas
By organisation
Mathematics (Div.)
In the same journal
The Electronic Journal of Combinatorics
Discrete Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 40 hits
ReferencesLink to record
Permanent link

Direct link