Further Results on Combinatorial Properties of Order-Preserving Alternating Semigroups.

Abstract

Let Cn be the charts on Xn = {1,2,...,n} be the alternating semigroups, OAnc be the subsemigroups of order preserving alternating semigroups and N(S) be the set of nilpotents element of a semigroups OAnc . Let G(n;p,m) = | {aeS : h(a) = p^f(a) = m }| ,G(n;m) = | {aeS : f(a) = m }| and G(p; m) = | {aeS : h(a) = p }| . In this paper, some combinatorial properties of OAnc for two parameters G(n; p) were discuss and their nilpotent elements were also investigated.