A381471 Number of non-isomorphic Dynkin systems on n points.

1, 1, 2, 3, 7, 13, 63, 838

Offset

0,3

Comments

A Dynkin system on a set S is a subset of the power set of S which contains the empty set, is closed under complements in S, and is closed under union of disjoint sets.

Links

Table of n, a(n) for n=0..7.

Martin Rubey and Peter Taylor, What is the number of finite Dynkin systems?, MathOverflow.

Wikipedia, Dynkin system

Formula

a(n) >= A000041(n).

Example

The a(3) = 3 representative systems are:
  {{}, {1,2,3}}
  {{}, {1}, {2,3}, {1,2,3}}
  {{}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}

Crossrefs

Cf. A000041, A380571 (labeled case).

Sequence in context: A051452 A058017 A049536 * A065508 A078154 A192611

Adjacent sequences: A381468 A381469 A381470 * A381472 A381473 A381474

Keyword

nonn,more

Author

Andrew Howroyd, Feb 26 2025

Status

approved