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Abstract: The number conn counts matchings X on f1; 2; : : : ; 2ng, 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 prove, using a more generally aplicable 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... (Update)
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BibTeX entry: (Update)
@misc{ klazar-non,
author = "Martin Klazar",
title = "On Non P-Recursiveness of Numbers of Matchings (Linear Chord Diagrams)
with Many Crossings",
url = "citeseer.ist.psu.edu/692989.html" }
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1 a class of linked diagrams, I. Enumeration (context) - Stein - 1978
1 a class of linked diagrams, II. Asymptotics (context) - Stein, Everett - 1978
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