Generating sets of strictly order-preserving transformation semigroups on a finite set
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Let On and POn denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set Xn = {1, . . . , n}, respectively. Then the strictly partial order-preserving transformation semigroup SPOn on the set Xn, under its natural or- der, is defined by SPOn = POn \ On. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for 2 r n − 1.
Abstract
Let On and POn denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set Xn = {1, . . . , n}, respectively. Then the strictly partial order-preserving transformation semigroup SPOn on the set Xn, under its natural or- der, is defined by SPOn = POn \ On. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for 2 r n − 1.
참고문헌 (11)
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