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

1, 2, 7, 68, 4619, 15621334

Offset: 0

Author

Peter J. Taylor, Feb 28 2025

Keywords

• nonn
• more

Comments

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.

References

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

Links

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

Crossrefs

Cf. A380571, A381472 (unlabeled case).

Programs

Python

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