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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.25229 |
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| _version_ | 1866916044431425536 |
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| author | Adžić, Miloš Jevtić, Filip D. |
| author_facet | Adžić, Miloš Jevtić, Filip D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25229 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Syntax Of Polytopal Projections: From Permutohedra To Associahedra Adžić, Miloš Jevtić, Filip D. Combinatorics 52B05, 18M65 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. |
| title | The Syntax Of Polytopal Projections: From Permutohedra To Associahedra |
| topic | Combinatorics 52B05, 18M65 |
| url | https://arxiv.org/abs/2605.25229 |