Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, January 12, 2006, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Samuel Zürcher

We consider 0/1 matrices and say that an n*n matrix A contains a k*l
matrix P (the pattern) if and only if we can find a submatrix B of A
(that is obtained by deleting rows and columns of A) so that (P)_{i,j} =
1 implies (B)_{i,j} = 1. Otherwise, we say that A avoids P.
For a given pattern P, we are interested in the maximum number of 1
entries that an n*n matrix can have avoiding the pattern P; written as
ex(n, P). This extremal function is known for all patterns with at most
four 1 entries and each one of those patterns is member in one of five
classes; we'll show examples for each of those classes and sketch some
of the proofs for the bounds on ex(n, P).
In a second part of the talk, we'll show reductions that can be used to
determine ex(n, P') for a pattern P' with previously unknown complexity,
based on the knowledge of the complexity of a somehow related pattern P.

This talk is mainly based on work by Tardos, Marcus, Füredi, Hajnal, and Keszegh.

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