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arXiv · 2605.25229

The Syntax Of Polytopal Projections: From Permutohedra To Associahedra

Miloš Adžić·Filip D. Jevtić
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Abstract

Tonks' projection from the permutohedron to the associahedron and the Loday--Ronco map both send permutations to planar binary trees. We give a syntactic account of these maps in the equational calculus of the free non-symmetric, non-unital operad on one binary generator. The vertex restriction of Tonks' projection is obtained by evaluating the head-insertion encoding on the reversed permutation, while the Loday--Ronco map is obtained by evaluating the decreasing encoding. We also give a local operadic proof that Tonks' vertex map is order-preserving from the weak Bruhat order to the Tamari order.

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Miloš Adžić, Filip D. Jevtić. 2026-05-24. The Syntax Of Polytopal Projections: From Permutohedra To Associahedra. https://arxiv.org/abs/2605.25229

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