OFFSET
0,2
COMMENTS
a(n) is the number of orbits for the corresponding families of maximal antichains (see also A326358) of the powerset of {1,2,...,n} under the action of the symmetry group S_n.
LINKS
Dmitry I. Ignatov, On the Number of Maximal Antichains in Boolean Lattices for n up to 7. Lobachevskii J. Math., 44 (2023), 137-146.
Dmitry I. Ignatov, Supporting iPython code and input files for generating and counting inequivalent maximal antichains for n up to 7 and related sequences, Github repository, sections 0,1,4
Dmitry I. Ignatov, Supporting iPython notebook: A348260.ipynb
Dmitry I. Ignatov, PDF of the supporting iPython notebook
EXAMPLE
The a(0)=1 maximal antichains is {}.
The a(1)=2 maximal antichains are {}, {1}.
The a(2)=3 maximal antichains {}, {1}{2}, {12}.
Representatives of the a(3)=5 maximal antichains are: {}, {1}{2}{3}, {12}{3}, {12}{13}{23}, {123}.
Representatives of the a(4)=10 maximal antichains are:
{}, {1}{2}{3}{4},
{12}{3}{4}, {12}{13}{23}{4},
{123}{4}, {12}{13}{24}{14}{24}{34},
{123}{14}{24}{34}, {123}{124}{34},
{123}{124}{134}{234}, {1234}.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Dmitry I. Ignatov, Oct 13 2021
STATUS
approved