Enumerative combinatorics
The combinatorics of q-Hermite polynomials and the Askey-Wilson integral
European Journal of Combinatorics
Symmetric functions and P-Recursiveness
Journal of Combinatorial Theory Series A
A bijective proof of a Touchard-Riordan formula
Proceedings of the 4th conference on Formal power series and algebraic combinatorics
Counting non-isomorphic chord diagrams
Theoretical Computer Science - Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger
On the number of chord diagrams
Discrete Mathematics
Bell numbers, their relatives, and algebraic differential equations
Journal of Combinatorial Theory Series A
Haruspicy 2: the anisotropic generating function of self-avoiding polygons is not D-finite
Journal of Combinatorial Theory Series A
Partitions and partial matchings avoiding neighbor patterns
European Journal of Combinatorics
Four-regular graphs with rigid vertices associated to DNA recombination
Discrete Applied Mathematics
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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.