Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
n! MATCHINGS, n! POSETS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
2011 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 2, 435-449 p.Article in journal (Refereed) Published
Abstract [en]

We show that there are n! matchings on 2n points without so-called left (neighbor) nestings. We also define a set of naturally labeled (2 + 2)-free posets and show that there are n! such posets on 71 elements. Our work was inspired by Bousquet-Melou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884-909]. They gave bijections between four classes of combinatorial objects: matchings with no neighbor nestings (due to Stoimenow), unlabeled (2 + 2)-free posets, permutations avoiding a specific pattern, and so-called ascent sequences. We believe that certain statistics on our matchings and posets could generalize the work of Bousquet-Melou et al., and we make a conjecture to that effect. We also identify natural subsets of matchings and posets that are equinumerous to the class of unlabeled (2 + 2)-free posets. We give bijections that show the equivalence of (neighbor) restrictions on nesting arcs with (neighbor) restrictions on crossing arcs. These bijections are thought to be of independent interest. One of the bijections factors through certain upper-triangular integer matrices that have recently been studied by Dukes and Parviainen [Electron. J. Combin. 17 (2010) #R53].

Place, publisher, year, edition, pages
2011. Vol. 139, no 2, 435-449 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-31598DOI: 10.1090/S0002-9939-2010-10678-0ISI: 000287283300006Scopus ID: 2-s2.0-78651286738OAI: oai:DiVA.org:kth-31598DiVA: diva2:406319
Funder
Knut and Alice Wallenberg Foundation
Note
QC 20110325Available from: 2011-03-25 Created: 2011-03-21 Last updated: 2017-12-11Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Linusson, Svante

Search in DiVA

By author/editor
Linusson, Svante
By organisation
Mathematics (Div.)
In the same journal
Proceedings of the American Mathematical Society
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 21 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf