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arXiv · 1711.05027

A note on Tamari intervals

Frédéric Chapoton
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Abstract

To every partial order P, one associates a polynomial $\mathbb{D}_P$ in 4 variables that enumerates the intervals of P according to 4 parameters. Some symmetry properties of this polynomial are obtained for a specific family of posets, the Tamari lattices. A ternary symmetry is proved for the polynomial in 3 variables obtained by setting one variable to 1. Another global symmetry is conjectured. The set of synchronized intervals is described using a facet of the Newton polytope. A relation to the statistics of the canopy of binary planar trees is described.

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Frédéric Chapoton. 2017-11-14. A note on Tamari intervals. https://arxiv.org/abs/1711.05027

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