## Discrete Math Seminar: Richard Anstee

- Date: 10/16/2018
- Time: 16:00

University of British Columbia

(0,1,2)-matrices can sometimes behave like (0,1)-matrices

This is joint work with Jeffrey Dawson, Linyuan Lu and Attila Sali.

We define simple matrices as those whose entries are chosen from {0,1,2} and for which no columns are repeated. We consider the extremal problem of how many columns can an m-rowed simple matrix A have, subject to the condition that A avoids certain submatrices.

We consider some forbidden submatrices (configurations) that seem to force A to behave like a (0,1)-matrix. Define T_k(a,b,c) to be the kxk matrix with b's on the diagonal, a's below the diagonal and c's above the diagonal. These generalize the identity and triangular matrices. There are such 8 matrices to forbid which seem to force A to behave like a (0,1)-matrix. Some preliminary results are given.

Location: ESB 4127