The structure of alternative tableaux

Details The structure of alternative tableaux The structure of alternative tableaux

2009-08-27

arxiv.org/abs/0908.4050v2

Mathematics

Combinatorics

23 pages. v2: minor corrections

Scientific paper

In this paper we study alternative tableaux introduced by Viennot. These tableaux are in simple bijection with permutation tableaux, defined previously by Postnikov . We exhibit a simple recursive structure for alternative tableaux. From this decomposition, we can easily deduce a number of enumerative results. We also give bijections between these tableaux and certain classes of labeled trees. Finally, we exhibit a bijection with permutations, and relate it to some other bijections that already appeared in the literature.

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