, RON FERGUSON AND ATTILA SALI, Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada; Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada and Mathematics Institute of Hungarian Academy of Sciences, Budapest, Hungary
|Small forbidden configurations|
An extremal set problem stated in matrix terms considers a (0,1)-matrix F and an (0,1)-matrix A which has no repeated columns. We assume A has no submatrix which is a row and column permutation of F and then seek bounds on n in terms of F,m. We wish to report progress in obtaining a number of new exact bounds for various F. The arguments often use graph theory in interesting ways. Turán's m2/4 bound arises with a different twist. It seems possible to get exact bounds for all F. Progress for F has also been obtained but the triple systems are harder to analyze.