| 压缩变换半群的一些组合性质 |
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| 引用本文： | 王永平,唐先聪,游泰杰. 压缩变换半群的一些组合性质[J]. 淮阴工学院学报, 2012, 21(1): 5-7 |
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| 作者姓名： | 王永平 唐先聪 游泰杰 |
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| 作者单位： | 1. 贵州师范大学数学与计算机科学学院,贵阳,550001
2. 淮阴工学院数理学院,江苏淮安,223003 |
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| 摘 要： | 设Tn是有限集Xn={1,2,…,n}上的变换半群。任取α∈Tn,若对任意的x、y∈Xn,有｜xα-yα｜≤｜x-y｜,则称α是Tn的压缩元。令CTn={α｜α是Tn的压缩元},容易验证CTn是Tn的子半群,称该半群为压缩变换半群。主要研究了CTn的组合性质,证明了｜CTn｜=n·3n-1-2∑n-1j=1LN1j.3n-1-j;LN1n=3LN1n-1-LNn-1（1,1）,n≥3;LN（1,1）n=2LN（1,1）n-1＋LN（1,321）n,n≥5。
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| 关 键 词： | 变换半群 压缩 组合性质 AdaBoost算法 |
On Combinatorial Property of Compressive Transformation Semigroup |
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| WANG Yong-ping,TANG Xian-cong,YOU Tai-jie. On Combinatorial Property of Compressive Transformation Semigroup[J]. Journal of Huaiyin Institute of Technology, 2012, 21(1): 5-7 |
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| Authors: | WANG Yong-ping TANG Xian-cong YOU Tai-jie |
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| Affiliation: | 1(1.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China; 2.Faculty of Mathematics and Physics,Huaiyin Institute of Technology,Huai’an Jiangsu 223003,China) |
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| Abstract: | Let be transformation semigroup on finite set Xn={1,2,…,n}.For all α∈Tn,we shall call α is compressive element of Tn if|xα-yα|≤|x-y| for all x,y in Xn.Let CTn be a set that consists of the compressive element of Tn.Then CTn is a subsemigroup of Tn,we call CTn as compressive semigroup.It is shown that |CTn|=n·3n-1-2∑n-1j=1LN1j·3n-1-j;LN1n=3LN1n-1-LNn-1(1,1),n≥3;LN(1,1)n=2LN(1,1)n-1+LN(1,321)n,n≥5. |
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| Keywords: | transformation semigroup compressive combinatorial property AdaBoost algorithm |
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