Discrete Math Seminar: Ruiyuan Chen
Date
-
Topic
Forbidden Submatrices
Speakers
Details
Abstract:
We consider an extremal problem arising from forbidding a submatrix. Let F be a given (0,1)-matrix. Let avoid(m,F) denote the set of m-rowed (0,1)-matrices with no repeated columns and no submatrix F. Here we are concerned with row and column order. Let f(m,F) denote the maximum number of columns among all matrices in avoid(m,F). A conjecture of Anstee, Frankl, Furedi and Pach is that if F has k row, then there is a constant c(F) so that f(m,F)<c(F)m^k. We make progress in the case k=2 using an `amortized' analysis. This represents joint work with Richard Anstee and Attila Sali.
We consider an extremal problem arising from forbidding a submatrix. Let F be a given (0,1)-matrix. Let avoid(m,F) denote the set of m-rowed (0,1)-matrices with no repeated columns and no submatrix F. Here we are concerned with row and column order. Let f(m,F) denote the maximum number of columns among all matrices in avoid(m,F). A conjecture of Anstee, Frankl, Furedi and Pach is that if F has k row, then there is a constant c(F) so that f(m,F)<c(F)m^k. We make progress in the case k=2 using an `amortized' analysis. This represents joint work with Richard Anstee and Attila Sali.
Additional Information
Location: MATX 1102
For more information please visit UBC mathematics department
Ruiyuan (Ronnie) Chen
