Products of idempotents in finite full transformation semigroups: some improved bounds
Products of idempotents in finite full transformation semigroups: some improved bounds
复制标题
有限全变换半群中幂等的乘积：一些改进的界限
DOI：
10.1017/s0308210500025531
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
J. Howie
中科院分区：
文献类型：
--
作者：
J. Howie
设E是S_n中的幂等元的集合，是{1，…的所有奇异自映射的半群，n}。对于锡中的每个α，都有一个唯一的(κ(α)≧1，使得αψEκ，(α)。已知周期n+κ(α)≦α-α，其中α是a的循环轨道数，Fixα是不动点的数。只有当a的秩为n-1时，等式才成立。得到了一个改进的上界(κ(α)，适用于任意秩元素。还得到了一个下界。
Synopsis Let E be the set of idempotents in Sn, the semigroup of all singular selfmaps of {1,…, n}. For each α in Sn, there is a unique (κ(α)≧1 such that αψEκ,(α). It is known that κ(α)≦ n + cycl α -fix α, where cyclα is the number of cyclic orbits of a and fix α is the number of fixed points. Equality holds only in the case where a is of rank n – 1. An improved upper bound is obtained for κ(α), applying to elements of arbitrary rank. A lower bound is obtained also.