On the essential test sets of discrete matrices

Abstract

We consider discrete matrices with distinct rows. A test set of a matrix is a subset of columns such that all the corresponding subrows are distinct. The essential test set of a matrix is the intersection of all the test sets. A relationship between the size of a matrix and the cardinality of the essential test set is derived. Also, we investigate matrices having essential test sets of maximum cardinality, and characterize a relationship of such matrices with trees.