The Latin Tableau Conjecture

2024/08/07 by Timothy Y. Chow, Chow, Timothy Y., Mark Tiefenbruck +1
Arts and Humanities · Social Sciences · #05C15 #Ancient Egypt and Archaeology #Combinatorics (math.CO) #FOS: Mathematics #Historical and Linguistic Studies #Language, Linguistics, Cultural Analysis

paper · pdf · doi:10.48550/arxiv.2408.04086

openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Latin tableau of shape λ and type μ is a Young diagram of shape λ in which each box contains a single positive integer, with no repeated integers in any row or column, and the ith most common integer appearing μ_i times. Over twenty years ago, Chow et al., in their study of a generalization of Rota's basis conjecture that they called the wide partition conjecture, conjectured a necessary and sufficient condition for the existence of a Latin tableau of shape λ and type μ. We report some computational evidence for this conjecture, and prove that the conjecture correctly characterizes, for any given λ, at least the first four parts of μ.

Related

• Wide partitions, Latin tableaux, and Rota's basis conjecture
• On the Existence of Tableaux with Given Modular Major Index
• Outline Rectangles, Allocations, and Latin Young Diagrams
• Isotopy graphs of Latin tableaux
• Enumeration of standard barely set-valued tableaux of shifted shapes