Joint CSMath Seminar Date: 23/05/2022 Day: Monday Time: 2 pm to 3:15 pm Venue: Seminar Hall Existence of transversal in a Latin rectangle Debsoumya Chakraborti The Institute for Basic Sciences, South Korea. 230522 Abstract A Latin square of order $n$ is an $n \times n$ array of $n$ symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of $n$ entries such that no two entries share the same row, column, or symbol. Transversals in Latin squares have been a classical research topic in combinatorics, dating back to the time of Euler, who studied conditions on when Latin squares can be decomposed into transversals. One of the central and longstanding conjectures in combinatorial design, attributed to Brualdi, Ryser, and Stein, states that every $n \times n$ Latin square has a partial transversal of size $n1$.
We show the existence of a transversal of size $n$ in every Latin
rectangle
