_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Aug 04 2000

proposed

approved

fini,full,nonn

approved

proposed

fini,nonn,new

Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Aug 04 2000

G. f. : Z(S_6 X S_6; x_1, x_2, ...)-2*Z(S_6 X S_5; x_1, x_2, ...)+Z(S_5 X S_5; x_1, x_2, ...) if we replace x_i by 1+x^i, where Z(S_i X S_j; x_1, x_2, ...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j, respectively.

fini,nonn,new

G. f. : Z(S_6 X S_6; x_1, x_2, ...)-2*Z(S_6 X S_5; x_1, x_2, ...)+Z(S_5 X S_5; x_1, x_2, ...) if we replace x_i by 1+x^i, where Z(S_i X S_j; x_1, x_2, ...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j, respectively.

fini,nonn,new

Number of 6x6 binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

G. f. : Z(S_6 X S_6; x_1,x_2,...)-2*Z(S_6 X S_5; x_1,x_2,...)+Z(S_5 X S_5; x_1,x_2,...) if we replace x_i by 1+x^i, where Z(S_i X S_j; x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j,respectively.

fini,nonn,new

6x6 binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

1, 2, 15, 69, 288, 840, 2144, 4488, 8317, 13160, 18636, 23078, 25856, 25623, 23187, 18713, 13932, 9288, 5816, 3256, 1767, 858, 419, 180, 88, 34, 16, 6, 3, 1, 1

6,2

Sum_{k=0..36} a(n)=A054976(6).

G. f. : Z(S_6 X S_6;x_1,x_2,...)-2*Z(S_6 X S_5;x_1,x_2,...)+Z(S_5 X S_5;x_1,x_2,...) if we replace x_i by 1+x^i, where Z(S_i X S_j;x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j,respectively.

Cf. A052370.

fini,nonn

Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 04 2000

approved