Width and dual width of subsets in polynomial association schemes
Width and dual width of subsets in polynomial association schemes
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DOI：
10.1016/s0097-3165(03)00006-2
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发表时间：
2003-05
期刊：
影响因子：
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通讯作者：
A. Brouwer;C. Godsil;J. Koolen;W. Martin
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文献类型：
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作者：
A. Brouwer;C. Godsil;J. Koolen;W. Martin
距离正则图的顶点的子集 C 的宽度是 C 的元素之间出现的最大距离。对偶而言，彗星关联方案中子集的对偶宽度是 Q 多项式排序中“最后”特征空间的索引，C 的特征向量与该特征空间不正交。基本界限是根据这两个新参数得出的。我们证明最小宽度的任何子集都是完全规则的代码，并且最小双宽度的任何子集都会在原始代码中引入彗星关联方案。考虑了各种示例和应用。
The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs between elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the “last” eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on these two new parameters. We show that any subset of minimal width is a completely regular code and that any subset of minimal dual width induces a cometric association scheme in the original. A variety of examples and applications are considered.