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.
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 52B05, 18M65 |
| Cite as: | arXiv:2605.25229 [math.CO] |
| (or arXiv:2605.25229v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25229 arXiv-issued DOI via DataCite (pending registration) |
From: Filip Jevtić [view email]
[v1]
Sun, 24 May 2026 19:31:50 UTC (294 KB)
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