A286874 Maximal number of binary vectors of length n such that the union (or bitwise OR) of any 2 distinct vectors does not contain any other vector.

1, 2, 2, 3, 4, 5, 6, 7, 8, 12, 13, 17

Offset

0,2

Comments

The concatenation of these vectors produces a 2-disjunct matrix.

a(10) >= 13. Here is a candidate solution: {0101000001 0001000110 1000100001 0010000011 1001010000 0010110000 1000001010 0011001000 0100100010 1110000000 0100010100 0000011001 0000101100}. - Dmitry Kamenetsky, Sep 07 2017

a(11) >= 17. Here is a candidate solution: {01000010100 10000100100 00000001110 00010010001 10000011000 01000001001 00001010010 00010101000 00100110000 00100000101 00000100011 00101001000 10110000000 11000000010 00011000100 10001000001 01001100000}. - Dmitry Kamenetsky, Sep 07 2017

The best lower bounds known for the next terms a(12)-a(16) are 20, 26, 28, 42 and 45 (see attached files for the solutions).

Links

Table of n, a(n) for n=0..11.

Johan V. Dinesen, Lower bound and solution for a(15)

Dmitry Kamenetsky, Lower bounds and their solutions for a(12-16)

Wikipedia, Disjunct Matrix

Example

Here is a solution for n=9: {110001000 001001010 001100100 100100010 100010100 000010011 101000001 011010000 000111000 010100001 010000110 000001101}.

Crossrefs

Cf. A054961, A303977 gives the number of distinct solutions.

Sequence in context: A001313 A057537 A339094 * A065459 A011873 A173151

Adjacent sequences: A286871 A286872 A286873 * A286875 A286876 A286877

Keyword

nonn,more

Author

Dmitry Kamenetsky, Aug 02 2017

Extensions

a(10)-a(11) from Zhao Hui Du, May 04 2018

Status

approved