PIMS-UVic Discrete Math Seminar: Alp Muyesser

A Latin square is an n by n grid filled with n symbols so that each symbol appears exactly once in every row and column. A transversal in a Latin square is a selection of entries with no row, column, or symbol repetition. The study of transversals in Latin squares is as old as combinatorics, going back to Euler's work in the 18th century. A lot of exciting progress has been made in this area in the past few years. In 2020, Kwan proved that, with high probability, a random Latin square contains a full transversal (hitting each row and column). In the other extreme, in 2022, Müyesser and Pokrovskiy characterised the "algebraic" Latin squares which contain full transversals. Very recently, Montgomery proved that all Latin squares contain a transversal hitting all but one row. A key technique that is used in each of these results is the "distributive absorption method", introduced in 2014 by Montgomery to find spanning trees in random graphs. In this talk, we will give a gentle introduction to this technique.