1,2

J. Kahn, J. Komlos, E. Szemeredi: On the probability that a random $\pm1$-matrix is singular, J. AMS 8 (1995), 223-240.

J. Komlos, On the determinant of (0,1)-matrices, Studia Math. Hungarica 2 (1967), 7-21.

N. Metropolis and P. R. Stein, On a class of (0,1) matrices with vanishing determinants, J. Combin. Theory, 3 (1967), 191-198.

Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

M. Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.

Index entries for sequences related to binary matrices

The probability that a random n X n {0,1}-matrix is singular is conjectured to be asymptotic to C(n+1, 2)*(1/2)^(n-1). [Corrected by njas, Jan 02 2007]

a(2)=10: the matrix of all 0's, 4 matrices with 2 zeros in the same row or column, 4 matrices with 3 zeros, and the all-1 matrix.

(PARI) A046747(n) = m=matrix(n, n); ct=0; for(x=0, 2^(n*n)-1, a=binary(x+2^(n*n)); for(i=1, n, for(j=1, n, m[i, j]=a[n*i+j+1-n])); if(matdet(m)==0, ct=ct+1, ); ); ct - from Randall L. Rathbun

A046747(n) = 2^(n^2) - n! * binomial(2^n -1, n) + n! * A000410(n). Cf. A000409, A002884.

Cf. also A056990, A056989, A046747, A055165, A002416.

Also a(n) + A055165(n) = 2^(n^2) = total number of n X n (0, 1) matrices, sequence A002416.

Sequence in context: A064343 A127823 A113082 this_sequence A006426 A029698 A060704

Adjacent sequences: A046744 A046745 A046746 this_sequence A046748 A046749 A046750

hard,nonn,nice

G"unter M. Ziegler (ziegler(AT)math.tu-berlin.de)

a(8) from Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 28 2006