2,2

This is a lower bound for the set of all n X n (0,1)-matrices having distinct, nonzero ordered rows and determinant 0 (compare A000410).

Here ordered means that we take only one representative from the n! matrices obtained by all permutations of the distinct rows of an n X n matrix.

a(n) is also the number of sets of n distinct nonzero (0,1)-vectors in R^n that do not span R^n.

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.

G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in preparation, 2004.

Index entries for sequences related to binary matrices

a(n) = -sum(stirling1(n+1, k+1)*binomial(2^k-1, n), k=0..n-1).

a(n) = binomial(2^n-1, n) - A094000(n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Nov 27 2005

with(combinat): T := proc(n) -sum(stirling1(n+1, k+1)*binomial(2^k-1, n), k=0..n-1); end proc:

Cf. A000410, A002884, A046747.

Sequence in context: A001509 A003031 A047941 this_sequence A059415 A002684 A036281

Adjacent sequences: A000406 A000407 A000408 this_sequence A000410 A000411 A000412

nonn,nice

njas

Edited by Edwin Clark (eclark(AT)math.usf.edu), Nov 02 2003