半群O_n(k,m)的秩

Ranks of the semigroup O_n(k,m)

设On是有限链[n]上的保序变换半群.对任意1≤k≤n-1且2≤m≤n,研究了半群On(k,m)={α∈On|kα≤k,mα≥m}的幂等元秩和秩.

Let O_n be the semigroup of all order-preserving transformations on a finite-chain[n].For an arbitrary integers k,m such that 1≤k≤n-1 and 2≤m≤n,the rank and idempotent rank of the semigroup O_n(k,m)={α∈ O_n|kα≤k,mα≥m}were studied.