Non-ambiguous trees: new results and generalisation (Full version)

03/12/2021

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by   Bérénice Delcroix-Oger, et al.

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We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential equation whose solution can be described combinatorially. This yields a new formula for the number of NATs. We also obtain q-versions of our formula. We finally generalise NATs to higher dimension.