cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Mark Bowron

Mark Bowron's wiki page.

Mark Bowron has authored 2 sequences.

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

Original entry on oeis.org

1, 2, 7, 114, 9602, 3962940, 7516789560, 62622777447552, 2221417812173570640
Offset: 0

Author

Mark Bowron, Apr 06 2025

Keywords

Comments

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).

Crossrefs

Cf. A382693 (without symmetry).

Extensions

a(8) from Christian Sievers, May 26 2025

A382693 Number of dense symmetric binary relations on {1,...,n}.

Original entry on oeis.org

1, 2, 4, 20, 234, 6308, 374586, 47740076, 12788143462, 7090729971308
Offset: 0

Author

Mark Bowron, Apr 03 2025

Keywords

Comments

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 symmetric 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.
Note that terms were added for n = 7 and 8 in a SeqFan post (see link).

Crossrefs

Cf. A382839 (with symmetry added).

Extensions

a(9) from Christian Sievers, May 26 2025