Forbidden Configurations, Discrepancy and Determinants

Fractional Weak Discrepancy of Posets and Certain Forbidden Configurations

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset subject to forbidden r+ s configurations, where r+s = 4. Generalizing previous work on weak discrepancy in [5, 12, 13], the notion of fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [7] as the minimum nonnegative k for which there exists a function f : V → R ...

Small Forbidden Configurations III

The present paper continues the work begun by Anstee, Ferguson, Griggs and Sali on small forbidden configurations. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. Let F be a k× l (0,1)-matrix (the forbidden configuration). Assume A is an m×n simple matrix which has no submatrix which is a row and column permutation of F . We define forb(m,F ) as the largest n, ...

Forbidden families of configurations

A simple matrix is a (0, 1)-matrix with no repeated columns. For a (0, 1)matrix F , we say that a (0, 1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F (trace is the set system version of a configuration). Let ‖A‖ denote the number of columns of A. Let F be a family of matrices. We define the extremal function forb(m,F) = max{‖A‖ : A is...

Small Forbidden Configurations II

The present paper continues the work begun by Anstee, Griggs and Sali on small forbidden configurations. In the notation of (0,1)-matrices, we consider a (0,1)-matrix F (the forbidden configuration), an m × n (0,1)-matrix A with no repeated columns which has no submatrix which is a row and column permutation of F , and seek bounds on n in terms of m and F . We give new exact bounds for some 2× ...

Linear Algebra and Forbidden Configurations