Séminaire Lotharingien de Combinatoire, 93B.20 (2025), 12 pp.

Andrew Reimer-Berg

Insertion Algorithms and Pattern Avoidance on Trees Arising in the Kapranov Embedding of M-0,n+3

Abstract. We answer a question of Gillespie, Griffin, and Levinson, that asks for a combinatorial bijection between two classes of trivalent trees, "Slide trees" and "Tournament trees" that are known via geometric arguments to be equinumerous. We define an insertion algorithm that gives a direct bijection between these two types of trees.

Secondly, we give a full classification of the Slide trees that are of caterpillar shape via pattern avoidance criteria.


Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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