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Bijective counting of tree-rooted maps and shuffles of parenthesis systems

Olivier Bernardi
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Abstract

The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long awaited) simple bijection which explains this result. We prove that our bijection is isomorphic to a former recursive construction on shuffles of parenthesis systems due to Cori, Dulucq and Viennot.

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Olivier Bernardi. 2006-01-27. Bijective counting of tree-rooted maps and shuffles of parenthesis systems. https://arxiv.org/abs/math/0601684

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