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正则(0,1)矩阵的行并存数
  • 时间:0
  • 分类:O151.21[理学—数学;理学—基础数学]
  • 作者机构:江西理工大学理学院,江西赣州341000
  • 相关基金:国家自然科学基金资助项目(11661041);江西省自然科学基金资助项目(20161BAB211016);江西省教育厅科技项目(GJJl50645)
作者: 钟金, 谷芳芳
中文摘要:

正则(0,1)矩阵是具有固定线和的(0,1)矩阵,为了更好的了解正则(0,1)矩阵的组合性质,研究了正则(0,1)矩阵的行并存数问题,给出了正则(0,1)矩阵行并存数的上下界,说明了在某些情形下该上界是精确的.此外,确定了行并存数为1的正则(0,1)矩阵类的行列式与奇异值.

英文摘要:

A regular (0, 1)-matrix is a (0, 1)-matrix which has constant line sums. In order to better understand the combinatorial properties of regular(0,1)-matrices, the row coincidence number problem of regular(0,1)- matrices is studied, upper and lower bounds for the row coincidence number of regular(0,1)-matrices are given, which shows that the upper bound is precise in some cases. Moreover, the determinants and singular values of the regular classes of (0, 1)-matrices are determined whose row coincidence numbers are 1.

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