有限满变换半群中3-路径的积

IF 0.3 Q4 MATHEMATICS, APPLIED
A. Imam, M. J. Ibrahim
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引用次数: 1

摘要

令Singn表示有限集合Xn={1,2,…的所有奇异自映射的半群。n}。如果有i, j, k∈Xn,使得对于所有x∈Xn\ {i, j}, iα=j,jα=k, xα=x,则映射α∈Singn称为3-path。在本文中,我们描述了一个将每个α∈Singn分解成3路径乘积的过程。每个factorisation的长度,这是许多因素在eachfactorisation,获得等于⌈12 (g(α)+ m(α))⌉,在g的重力(α)被称为α和m(α)是一个参数介绍了这工作,称为α的测量。进一步证明了Singn≥≥P[n−1],其中P为Singn中所有3路径的集合,且P[k]=P∪P2∪···∪Pk。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On products of 3-paths in finite full transformation semigroups
Let Singn denotes the semigroup of all singular self-maps of a finite set Xn={1,2, . . . , n}. A map α∈Singn is called a 3-path if there are i, j, k∈Xn such that iα=j,jα=k and xα=x for all x∈Xn\ {i, j}. In this paper, we described aprocedure to factorise each α∈Singn into a product of 3-paths. The length of each factorisation, that is the number of factors in eachfactorisation, is obtained to be equal to ⌈12(g(α)+m(α))⌉, where g(α) is known as the gravity of α and m(α) is a parameter introduced inthis work and referred to as the measure of α. Moreover, we showed that Singn⊆P[n−1], where P denotes the set of all 3-paths in Singn and P[k]=P∪P2∪ ··· ∪Pk.
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来源期刊
Algebra & Discrete Mathematics
Algebra & Discrete Mathematics MATHEMATICS, APPLIED-
CiteScore
0.50
自引率
0.00%
发文量
11
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