Discrete Math Seminar: Richard Anstee

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.