Abstract
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 ${3\cdot2^{n-1}\over (n+1)(n+2)} \big({2n \atop n}\big)$, 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.
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