A116506 -id:A116506 - cp's OEIS frontend

A116532 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct, up to permutation of rows.

0, 0, 3, 285, 50820, 23551920, 31898503077, 134251404794199

Offset: 1

Vladeta Jovovic, Apr 03 2006

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

a(n) = A054780(n) - A088389(n).

A000410 Number of singular n X n rational (0,1)-matrices.

Original entry on oeis.org

0, 0, 6, 425, 65625, 27894671, 35716401889, 144866174953833

Offset: 1

N. J. A. Sloane

Number of all n X n (0,1)-matrices having distinct, nonzero ordered rows and determinant 0 - compare A000409.

a(n) is the number of singular n X n rational {0,1}-matrices with no zero rows and with all rows distinct, up to permutation of rows and so a(n) = binomial(2^n-1,n) - A088389(n). Cf. A116506, A116507, A116527, A116532. - Vladeta Jovovic, Apr 03 2006

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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, arXiv:math/0511636 [math.CO], 2005.
Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.
Index entries for sequences related to binary matrices

Cf. A000409, A046747, A064230, A064231.

n! * a(n) = A046747(n) - 2^(n^2) + n! * binomial(2^n -1, n).

n=7 term from Guenter M. Ziegler (ziegler(AT)math.TU-Berlin.DE)

a(8) from Vladeta Jovovic, Mar 28 2006

A116527 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.

Original entry on oeis.org

0, 0, 0, 75, 22365, 13303500, 21058940420, 98692672142610

Offset: 1

Vladeta Jovovic, Apr 03 2006

Cf. A000409, A000410, A116506, A116507, A116532.

a(n) = A094000(n) - A088389(n).

Conjecture: a(n) = A000410(n) - A000409(n-1) for n>1. - Jean-François Alcover, Jan 08 2020

A116507 Number of singular n X n rational {0,1}-matrices with no zero rows or columns.

Original entry on oeis.org

0, 1, 91, 18943, 12483601, 28530385447, 235529139302185, 7183142489571818623

Offset: 1

Vladeta Jovovic, Apr 03 2006

Cf. A000410, A116506, A116527, A116532.

a(n) = A048291(n) - A055165(n).

cp's OEIS Frontend

A116532 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct, up to permutation of rows.

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A000410 Number of singular n X n rational (0,1)-matrices.

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A116527 Number of singular n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.

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A116507 Number of singular n X n rational {0,1}-matrices with no zero rows or columns.

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