On the maximum rank of completions of entry pattern matrices.

In an entry pattern matrix A , all entries are indeterminates but the same indeterminate can appear in numerous positions. For a field F , an F -completion of A results from assigning a value from F to each indeterminate entry. We define the generic F -rank of an entry pattern matrix to be its rank when considered over the function field generated over F by its indeterminate entries. We investigate the situation where the generic F -rank of A is not attained by any F -completion of A , which can occur only if the generic F -rank exceeds the field order. [ABSTRACT FROM AUTHOR]