Frederik Garbe: Limits of Sequences of Latin Squares

Speaker:Frederik Garbe

Title: Limits of Sequences of Latin Squares

Abstract: We introduce a limit theory for sequences of Latin squares paralleling the ones for dense graphs and permutations. The limit objects are certain distribution valued two variable functions, which we call Latinons, and left-convergence is defined via densities of kxl subpatterns of Latin Squares. The main result is a compactness theorem stating that every sequence of Latin squares of growing orders has a Latinon as an accumulation point. Furthermore, our space of Latinons is minimal, as we show that every Latinon can be approximated by Latin squares. This relies on a result of Keevash about combinatorial designs. We also introduce an analogue of the cut-distance and prove counterparts to the counting lemma, sampling lemma and inverse counting lemma.

This is joint work with R. Hancock, J. Hladky, and M. Sharifzadeh.