Search: id:A046747
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%I A046747
%S A046747 1,10,338,42976,21040112,39882864736,292604283435872,
%T A046747 8286284310367538176
%N A046747 Number of n X n rational {0,1}-matrices of determinant 0.
%D A046747 J. Kahn, J. Komlos, E. Szemeredi: On the probability that a random $\pm1$-matrix 
               is singular, J. AMS 8 (1995), 223-240.
%D A046747 J. Komlos, On the determinant of (0,1)-matrices, Studia Math. Hungarica 
               2 (1967), 7-21.
%D A046747 N. Metropolis and P. R. Stein, On a class of (0,1) matrices with vanishing 
               determinants, J. Combin. Theory, 3 (1967), 191-198.
%D A046747 Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra 
               and its Applications, 414 (2006), 310-346.
%H A046747 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SingularMatrix.html">Link to a section of The World of Mathematics.</
               a>
%H A046747 M. Zivkovic, <a href="http://arXiv.org/abs/math.CO/0511636">Classification 
               of small (0,1) matrices</a>, Linear Algebra and its Applications, 
               414 (2006), 310-346.
%H A046747 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%F A046747 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 N. J. A. 
               Sloane (njas(AT)research.att.com), Jan 02 2007]
%e A046747 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.
%o A046747 (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
%Y A046747 A046747(n) = 2^(n^2) - n! * binomial(2^n -1, n) + n! * A000410(n). Cf. 
               A000409, A002884.
%Y A046747 Cf. also A056990, A056989, A046747, A055165, A002416.
%Y A046747 Also a(n) + A055165(n) = 2^(n^2) = total number of n X n (0, 1) matrices, 
               sequence A002416.
%Y A046747 Sequence in context: A064343 A127823 A113082 this_sequence A006426 A029698 
               A060704
%Y A046747 Adjacent sequences: A046744 A046745 A046746 this_sequence A046748 A046749 
               A046750
%K A046747 hard,nonn,nice
%O A046747 1,2
%A A046747 G"unter M. Ziegler (ziegler(AT)math.tu-berlin.de)
%E A046747 a(8) from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 28 2006

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