A348260 Number of inequivalent maximal antichains of the Boolean lattice on a set of n elements.

1, 2, 3, 5, 10, 30, 233, 35925

Offset: 0

Author

Dmitry I. Ignatov, Oct 13 2021

Keywords

• nonn
• more

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.

Examples

			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}.
		

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

Crossrefs

Cf. A003182 (not necessarily maximal), A326358 (labeled case).

Cf. A326359, A326360.