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.
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.