Associated Permutations of Complete Non-Ambiguous Trees

Daniel Chen; Sebastian Ohlig

doi:10.46298/dmtcs.11169

Daniel Chen ; Sebastian Ohlig - Associated Permutations of Complete Non-Ambiguous Trees

dmtcs:11169 - Discrete Mathematics & Theoretical Computer Science, April 3, 2024, vol. 25:2 - https://doi.org/10.46298/dmtcs.11169

Associated Permutations of Complete Non-Ambiguous TreesArticle

Authors: Daniel Chen ; Sebastian Ohlig

We explore new connections between complete non-ambiguous trees (CNATs) and permutations. We give a bijection between tree-like tableaux and a specific subset of CNATs. This map is used to establish and solve a recurrence relation for the number of tree-like tableaux of a fixed size without occupied corners, proving a conjecture by Laborde-Zubieta. We end by establishing a row/column swapping operation on CNATs and identify new areas for future research.

https://doi.org/10.46298/dmtcs.11169

Source: arXiv.org:2210.11117

Volume: vol. 25:2

Section: Combinatorics

Published on: April 3, 2024

Accepted on: November 15, 2023

Submitted on: April 8, 2023

Keywords: Mathematics - Combinatorics

Licence: Attribution 4.0 International (CC BY 4.0)