Combinatoric results for graphical enumeration and the higher Catalan numbers

Details Combinatoric results for graphical enumeration and the higher Catalan numbers Combinatoric results for graphical enumeration and the higher Catalan numbers

2007-03-06

arxiv.org/abs/math/0703160v1

Mathematics

Combinatorics

9 pages, 2 figures

Scientific paper

We summarize some combinatoric problems solved by the higher Catalan numbers. These problems are generalizations of the combinatoric problems solved by the Catalan numbers. The generating function of the higher Catalan numbers appeared recently as an auxiliary function in enumerating maps and explicit computations of the asymptotic expansion of the partition function of random matrices in the unitary ensemble case. We give combinatoric proofs of the formulas for the number of genus 0 and genus 1 maps.

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