Max Aires, Rutgers University

Abstract

A configuration is a 0,1-matrix where rows are seen as points and columns as sets. Many problems in extremal combinatorics can be seen through the lens of configurations, such as Turan numbers and the Sauer-Shelah Theorem. We shall introduce the basic method of Standard Induction, and prove a foundational result of Balogh and Bollobas, then use these for a generalization of the extremal number of the 4-cycle, as well as discussing some other problems.