半群OI_n(k)的秩

Ranks of the Semigroup OI_n(k)

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,研究半群OI_n(k)={α∈OI_n:(■x∈dom(α))x≤k■xα≤k}的秩,证明了半群OI_n(k)的秩为n+1.

Abstract： Let OIn be the order-preserving injective partial transformation semigroup on [n]. For an arbitrary integer k such that 1≤k≤n-1, the rank of the semigroup OI_n（k）={α∈OI_n：（x∈dom（α））x≤k xα≤k} were studied. We show that the rank of semigroup OIn（k） is equal to n ＋ 1.