A382693 -id:A382693 - cp's OEIS frontend

A382839 Number of dense binary relations on {1,...,n}.

1, 2, 7, 114, 9602, 3962940, 7516789560, 62622777447552, 2221417812173570640

Offset: 0

Mark Bowron, Apr 06 2025

A binary relation R is usually called dense if for all R-related x and y there exists z such that x and z and also z and y are R-related (see Wikipedia link), but here we define a binary relation R on {1,...,n} to be "dense" (see the second page of the paper in the links) iff for all x and y we have (zRx implies zRy for all z) implies (x <= y).
Equivalently, as mentioned in a SeqFan post (see link), for all x < y, some z satisfies (not zRx) AND zRy.
Brendan McKay added terms for n = 6 and 7 in a SeqFan post (see link).

Francesco Ciraulo and Giovanni Sambin, The overlap algebra of regular opens, Journal of Pure and Applied Algebra, Volume 214, Issue 11, November 2010, Pages 1988-1995.
Seqfan, number of dense symmetric binary relations on {1,...,n} (A382693) and also.
Wikipedia, Dense Order, Generalizations.

Cf. A382693 (without symmetry).

a(8) from Christian Sievers, May 26 2025

cp's OEIS Frontend

A382839 Number of dense binary relations on {1,...,n}.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions