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
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
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.