半群OI_n(k,m)的秩

Ranks of the Semigroup OI_n( k,m)

设OI_n是[n]上的保序严格部分一一变换半群.对任意1≤k≤n-1,且2≤m≤n,研究半群OI_n(k,m)={α∈OI_n:(x,y∈dom(α))x≤k■xα≤k,y≥m■yα≥m}的秩,证明半群OI_n(k,k+1)的秩为n,且半群OI_n(k,m)(m≠k+1)的秩为n+2.

Let OInbe the order-preserving injective partial transformation semigroup on[n].For arbitrary integers k,m such that1≤k≤n-1 and 2≤m≤n,the rank of the semigroup OIn（k,m）={α∈OIn：（x,y∈dom（α））x≤k xα≤k,y≥m yα≥m}is studied.It is proved that the rank of semigroup OIn（k,k＋1）is n and the rank of semigroup OIn（k,m）（m≠k＋1）is n＋2.