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arXiv · 2607.01206

Decomposition of Greedy Tamari Intervals and Bipartite Planar Maps

Philippe Biane·Wenjie Fang
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Abstract

The greedy Tamari poset, inspired by the well-studied Tamari lattice, was recently defined by Dermenjian in the more general setting of greedy $\nu$-Tamari posets. Bousquet-M\'elou and Chapoton counted intervals of the greedy $m$-Tamari poset in 2024 by solving a functional equation, and found that they are equi-enumerous to planar $(m+1)$-constellations. In this work, we give a combinatorial proof of this fact for the case $m = 1$, which also gives the refined enumeration conjectured by Bousquet-M\'elou and Chapoton. This is done by establishing a recursive decomposition of greedy Tamari intervals isomorphic to that of bipartite planar maps. We also propose a more general and refined conjecture for the case of general $m$.

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Philippe Biane, Wenjie Fang. 2026-07-01. Decomposition of Greedy Tamari Intervals and Bipartite Planar Maps. https://arxiv.org/abs/2607.01206

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