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. Together with the work of Chang, Fuchs, Liu, Wallner, and Yu, our result verifies a conjecture of Pons and Batle on tree-child networks. This conjecture had been regarded as a specific and challenging problem in the phylogenetics community until its resolution in the present work.
From: FeiHu Liu [view email]
[v1]
Wed, 14 Jan 2026 15:09:39 UTC (233 KB)
[v2]
Thu, 15 Jan 2026 12:35:38 UTC (233 KB)
[v3]
Sun, 6 Sep 2026 11:49:29 UTC (239 KB)
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