All group-based latin squares possess near transversals
arXiv:1905.07071
summary
The paper proves that every latin square that is main‑class equivalent to a finite group’s Cayley table contains a near transversal, confirming the Brualdi‑Ryser‑Stein conjecture for this class of latin squares.
Abstract
In a latin square of order $n$, a near transversal is a collection of $n-1$ cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein asserts that every latin square possesses a near transversal. We show that this conjecture is true for every latin square that is main class equivalent to the Cayley table of a finite group.
Topics & keywords
#latin squares#near transversals#group-based latin squares#cayley tables#combinatorial designnear transversallatin squarefinite groupCayley tablemain class equivalenceBrualdi-Ryser-Stein conjecture