  We initiate a study of the zero-nonzero patterns of n by n alternating sign
matrices. We characterize the row (column) sum vectors of these patterns and
determine their minimum term rank. In the case of connected alternating sign
matrices, we find the minimum number of nonzero entries and characterize the
case of equality. We also study symmetric alternating sign matrices, in
particular, those with only zeros on the main diagonal. These give rise to
alternating signed graphs without loops, and we determine the maximum number of
edges in such graphs. We also consider n by n alternating sign matrices whose
patterns are maximal within the class of all n by n alternating sign matrices.

Combinatorics