Treffer: Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings
Title:
Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings
Authors:
Source:
Special Issue on Formal Power Series and Algebraic Combinatorics in Memory of Rodica Simion, 1995-2000Advances in applied mathematics (Print). 30(1-2):126-136
Publisher Information:
San Diego, CA: Elsevier, 2003.
Publication Year:
2003
Physical Description:
print, 30 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Problèmes combinatoires classiques, Classical combinatorial problems, Combinatoire, Combinatorics, Combinatoria, Concordance, Concordancia, Enumération, Enumeration, Enumeración, Equation différentielle, Differential equation, Ecuación diferencial, Fonction génératrice, Generating function, Función generatriz, Inversion, Inversión, Diagramme à cord linéaire, linear chord diagram, Nombre Catalan, Catalan number, P récursivité, P recursiveness, Série Laurent, Laurent series, Serie Laurent
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Applied Mathematics (KAM) and Institute for Theoretical Computer Science (ITI), Charles University, Malostranské Náméstí 25, 11800 Praha, Czech Republic
ISSN:
0196-8858
Rights:
Copyright 2003 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.14746797
Database:
PASCAL Archive
Weitere Informationen
The number conn counts matchings X on {1, 2, ..., 2n}, which are partitions into n two-element blocks, such that the crossing graph of X is connected. Similarly, cron counts matchings whose crossing graph has no isolated vertex. (If it has no edge, Catalan numbers arise.) We apply generating functions techniques and prove, using a more generally applicable criterion, that the sequences (conn ) and (cron) are not P-recursive. On the other hand, we show that the residues of conn and cron modulo any fixed power of 2 can be determined P-recursively. We consider also the numbers scon of symmetric connected matchings. Unfortunately, their generating function satisfies a complicated differential equation which we cannot handle.