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A231428 Sorted and encoded binary matrices representing equivalence relations. 7
0, 1, 2, 4, 7, 8, 12, 16, 18, 25, 32, 33, 42, 52, 63, 64, 68, 80, 96, 116, 128, 130, 136, 160, 170, 193, 225, 256, 257, 264, 272, 281, 322, 338, 388, 396, 455, 512, 513, 514, 516, 519, 584, 588, 656, 658, 729, 800, 801, 874, 948, 1023, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The N X N binary matrix of an equivalence relation is perfectly defined by its upper-right triangle. We encode such a matrix with the (N*(N-1))/2 bit number obtained by joining together each line of the upper-right triangle. The numbers are converted to base 10.

This is an infinite sequence and can be used for arbitrarily large values of N. To enumerate the finite list of n X n matrices for a given n, truncate this sequence to the first A000110(n) elements.

LINKS

Philippe Beaudoin, Table of n, a(n) for n = 1..10000

Philippe Beaudoin, Python program to generate the sequence

Tilman Piesk, Illustrated list of the first 52 equivalence relations

Tilman Piesk, Non-singleton blocks of the partitions of {1...8} in the same order.

Tilman Piesk, Permutations and partitions in the OEIS (Wikiversity)

EXAMPLE

The 4 X 4 equivalence matrices are represented by the first A000110(4) = 15 elements, that is: 0, 1, 2, 4, 7, 8, 12, 16, 18, 25, 32, 33, 42, 52, 63.

The 4 X 4 matrix corresponding to 25 = 0b011001 is:

  1 0 1 1

  0 1 0 0

  1 0 1 1

  1 0 1 1

CROSSREFS

Sequence in context: A233271 A088413 A090669 * A263660 A215822 A079374

Adjacent sequences:  A231425 A231426 A231427 * A231429 A231430 A231431

KEYWORD

nonn

AUTHOR

Philippe Beaudoin, Nov 09 2013

STATUS

approved

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Last modified December 8 02:07 EST 2016. Contains 278902 sequences.