The number of zeros of a tight sign-central matrix

In this paper, we determine the maximum number and the minimum number of zero entries of an m × n tight sign-central matrix with no zero rows for each pair (m, n) of positive integers with m + 1 ⩽ n ⩽ 2m. We also determine the maximum sparsity of tight sign-central matrices with m nonzero rows in terms of m for each positive integer m.