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Bijective Counting of Involutive Baxter Permutations

Fusy E.

Fundamenta Informaticae

2012

Vol. 117, nr 1-4

179-188

We enumerate bijectively the family of involutive Baxter permutations according to various parameters; in particular we obtain an elementary proof that the number of involutive Baxter permutations of size 2n with no fixed points is...[formula], a formula originally discovered by M. Bousquet-Melou using generating functions. The same coefficient also enumerates planar maps with n edges, endowed with an acyclic orientation having a unique source, and such that the source and sinks are all incident to the outer face.