Insertion algorithms and pattern avoidance on trees arising in the Kapranov embedding of $\overline{M}_{0,n+3}$
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908335735832576 |
|---|---|
| author | Reimer-Berg, Andrew |
| author_facet | Reimer-Berg, Andrew |
| contents | We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli space $\overline{M}_{0,n+3}$ of stable genus zero curves with $n+3$ marked points. Each set of trees enumerates the same intersection product of certain pullbacks of $ψ$ classes under forgetting maps.
We give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm. We also classify the words that appear on the slide trees of caterpillar shape via pattern avoidance conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Insertion algorithms and pattern avoidance on trees arising in the Kapranov embedding of $\overline{M}_{0,n+3}$ Reimer-Berg, Andrew Combinatorics Algebraic Geometry 05E14 (Primary) 05A05, 05C05, 14N10, 14H10 (Secondary) We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli space $\overline{M}_{0,n+3}$ of stable genus zero curves with $n+3$ marked points. Each set of trees enumerates the same intersection product of certain pullbacks of $ψ$ classes under forgetting maps. We give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm. We also classify the words that appear on the slide trees of caterpillar shape via pattern avoidance conditions. |
| title | Insertion algorithms and pattern avoidance on trees arising in the Kapranov embedding of $\overline{M}_{0,n+3}$ |
| topic | Combinatorics Algebraic Geometry 05E14 (Primary) 05A05, 05C05, 14N10, 14H10 (Secondary) |
| url | https://arxiv.org/abs/2504.17098 |