Proof of a Conjecture on Young Tableaux with Walls
Combinatorics
2026-01-16 v2
Abstract
Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by Chang, Fuchs, Liu, Wallner, and Yu leads to the verification of a conjecture on tree-child networks proposed by Pons and Batle. This conjecture was regarded as a specific and challenging problem in the Phylogenetics community until it was finally resolved by the present work.
Keywords
Cite
@article{arxiv.2601.09551,
title = {Proof of a Conjecture on Young Tableaux with Walls},
author = {Zhicong Lin and Feihu Liu and Jiahang Liu and Jing Liu and Guoce Xin},
journal= {arXiv preprint arXiv:2601.09551},
year = {2026}
}
Comments
38 pages, 11 figures