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

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

Offset: 0

Author

Andrew Howroyd, Feb 26 2025

Keywords

• nonn
• more

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.

Examples

			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}}
		

Links

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

Crossrefs

Cf. A000041, A380571 (labeled case).

Formula

a(n) >= A000041(n).