기초과학연구원 이산수학그룹
On September 24, 2024, Gábor Tardos from the Rényi Institute of Mathematics gave a talk at the Discrete Math Seminar on the extremal problems on 0-1 matrices. The title of his talk was “Extremal theory of 0-1 matrices“.
We say that a 0-1 matrix A contains another such matrix (pattern) P if P can be obtained from a submatrix of A by possibly changing a few 1 entries to 0. The main question of this theory is to estimate the maximal number of 1 entries in an n by n 0-1 matrix NOT containing a given pattern P. This question has very close connections to Turan type extremal graph theory and also to the Devenport-Schinzel theory of sequences. Results in the extremal theory of 0-1 matrices proved useful in attacking problems in far away fields as combinatorial geometry and the analysis of algorithms.
This talk will concentrate on acyclic patterns and survey some old and recent results in the area and will also contain several open problems.