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

1, 2, 7, 68, 4619, 15621334

Offset

0,2

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

Table of n, a(n) for n=0..5.

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

Prog

(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<<a):
                for b in range(a+1, 2**n):
                    if p&(1<<b):
                        if (a&b)==0 and not p&(1<<(a|b)):
                            break
                else:
                    continue
                break
        else:
            cnt+=1
    return cnt
# Bert Dobbelaere, Mar 16 2025

Crossrefs

Cf. A380571, A381472 (unlabeled case).

Sequence in context: A322223 A173226 A094223 * A376678 A217069 A323673

Adjacent sequences: A381572 A381573 A381574 * A381576 A381577 A381578

Keyword

nonn,more

Author

Peter J. Taylor, Feb 28 2025

Status

approved