proposed

approved

editing

proposed

Cf. A133687, A133686, A140637, A355529, A367867, A370583, A370636, A370640.

Cf. A072639, A326031, A355740, A367905, A367909, A368094, A368109.

Cf. A133686, A133687, A140637, A355529, A367867, A370583, A370587, A370636, A370640.

A326031 gives weight of the set-system with BII-number n.

Cf. A072639, ~A355739, `A326031, A355740, `A367772, A367905, A367909, A367912, A368094, `A368095, A368109.

Cf. A133686, A140637, `A134964, A355529, A370583, `A370587, A370636, ~A370638, `A370639, `A370640, ~A370641.

allocated for Gus WisemanNumber of subsets of {2..n} such that it is not possible to choose a different binary index of each element.

0, 0, 0, 0, 0, 1, 7, 23, 46, 113, 287, 680, 1546, 3374, 7191, 15008

0,7

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

The a(0) = 0 through a(7) = 23 subsets:

. . . . . {2,3,4,5} {2,4,6} {2,4,6}

{2,3,4,5} {2,3,4,5}

{2,3,4,6} {2,3,4,6}

{2,3,5,6} {2,3,4,7}

{2,4,5,6} {2,3,5,6}

{3,4,5,6} {2,3,5,7}

{2,3,4,5,6} {2,3,6,7}

{2,4,5,6}

{2,4,5,7}

{2,4,6,7}

{2,5,6,7}

{3,4,5,6}

{3,4,5,7}

{3,4,6,7}

{3,5,6,7}

{4,5,6,7}

{2,3,4,5,6}

{2,3,4,5,7}

{2,3,4,6,7}

{2,3,5,6,7}

{2,4,5,6,7}

{3,4,5,6,7}

{2,3,4,5,6,7}

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Table[Length[Select[Subsets[Range[2, n]], Select[Tuples[bpe/@#], UnsameQ@@#&]=={}&]], {n, 0, 10}]

The case with ones allowed is A370637, differences A370589.

The minimal case is A370644, with ones A370642.

A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

A058891 counts set-systems, A003465 covering, A323818 connected.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

A326031 gives weight of the set-system with BII-number n.

Cf. A072639, ~A355739, `A355740, `A367772, A367905, A367909, A367912, A368094, `A368095, A368109.

Cf. A133686, A140637, `A134964, A355529, A370583, `A370587, A370636, ~A370638, `A370639, `A370640, ~A370641.

allocated

nonn,more

Gus Wiseman, Mar 10 2024

approved

editing

allocated for Gus Wiseman

allocated

approved