A380571 -id:A380571 - cp's OEIS frontend

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

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

Offset: 0

Andrew Howroyd, Feb 26 2025

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.

			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}}

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

Cf. A000041, A380571 (labeled case).

a(n) >= A000041(n).

A381575 Number of disjoint-union partial algebras with zero on [n].

Original entry on oeis.org

1, 2, 7, 68, 4619, 15621334

Offset: 0

Peter J. Taylor, Feb 28 2025

A disjoint-union partial algebra on a set S is a subset of the power set of S which is closed under union of disjoint sets.
A disjoint-union partial algebra with zero on a set S is a disjoint-union partial algebra on S which contains the empty set.
There are twice as many disjoint-union partial algebras on S as disjoint-union partial algebras with zero on S because the disjoint-union partial algebras without the empty set can be placed in bijection with those which have the empty set.

Hirsch, R., & McLean, B. (2017). Disjoint-union partial algebras. Logical Methods in Computer Science, 13.

Robin Hirsch and Brett McLean, Disjoint-union partial algebras, arXiv:1612.00252 [math.RA], 2016-2017.

Cf. A380571, A381472 (unlabeled case).

def A381575(n):
    cnt=0
    for p in range(1,2**(2**n),2):
        for a in range(1,2**n):
            if p&(1<Bert Dobbelaere, Mar 16 2025

cp's OEIS Frontend

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

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