It is known that the semigroup Sing n of all singular self-maps of X n  = {1,2,â¦, n} has rank n(n â 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 19873. Gomes , G. M. S. , Howie , J. M. ( 1987 ). On the rank of certain finite semigroups of transformations . Math. Proc. Cambridge Phil. Soc. 101 : 395 - 303 .[CrossRef], [Web of Science ®]View all references.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ayi k et al. (20052. Ayık , G. , Ayık , H. , Howie , J. M. ( 2005 ). On factorisations and generators in transformation semigroups . Semigroup Forum 70 : 225 - 237 .[CrossRef], [Web of Science ®]View all references). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n â 1)/2.View full textDownload full textKey WordsFull transformation semigroup, Idempotent, Rank2000 Mathematics Subject Classification20M20Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870802067658
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机译：已知X n Â= {1,2，…，n}的所有奇异自映射的半群Sing n 的等级为n（n 1 1）/ 2。幂等等级定义为生成Sing n 的最小幂等数，其值与等级相同。 （请参阅Gomes和Howie，19873年。Gomes，GMS，Howie，JM（1987年）。关于变换的某些有限半群的秩。Math.Proc.Cambridge Phil.Soc.101：395-303。[CrossRef]，[Web （查看所有参考文献。）生成Sing n 的幂等性可以视为（m，r）-路径循环的特殊情况（m = r = 2），如Ayi k等。 （20052.Ayık，G.，Ayık，H.，Howie，JM（2005）。转换半群中的因式分解和生成器。Semigroup Forum 70：225-237。[CrossRef]，[Web ofScience®]查看所有参考）。本文的目的是表明，对于固定的m和r，Sing n 的（m，r）秩被定义为（m，r）个路径循环的最小数目生成Sing n 再次是n（nâ1）/ 2。查看全文下载全文关键字完全变换半群，幂等，Rrank2000数学主题分类20M20相关的var addthis_config = {ui_cobrand：“ Taylor＆弗朗西斯在线”，services_compact：“ citeulike，netvibes，twitter，technorati，美味，linkedin，facebook，stumbleupon，digg，google，更多”，发布号：“ ra-4dff56cd6bb1830b”};添加到候选列表链接永久链接http://dx.doi.org/10.1080/00927870802067658
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