TURKISH JOURNAL OF MATHEMATICS, cilt.45, sa.4, ss.1626-1634, 2021 (SCI-Expanded)
Let C-n be the semigroup of all order-preserving and decreasing transformations on X = {1, ..., n} under its natural order, and let N(C-n) be the subsemigroup of all nilpotent elements of C-n. For 1 <= r <= n - 1, let