BooleanLattice

The poset of subsets of $\{1,\dots,n\}$ ordered by inclusion, on which MoebiusFunction gives the signs of inclusion–exclusion.

BooleanLattice(n)subsets of $\{1,\dots,n\}$ ordered by inclusion

Typed signatures

Type	Package	Applies
(integer) -> expression<BooleanLattice>	incidence	always

Domain: Incidence algebras

Examples

Basic #

Subsets of $\{1,2\}$

live ↗

In$\mathrm{PosetElements}(\mathrm{BooleanLattice}(2))$Out$\bigl\lbrack\bigl\lbrack\bigr\rbrack, \bigl\lbrack1\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack1, 2\bigr\rbrack\bigr\rbrack$

$(-1)^3$

live ↗

In$\mathrm{MoebiusFunction}(\mathrm{BooleanLattice}(3), \bigl\lbrack\bigr\rbrack, \bigl\lbrack1, 2, 3\bigr\rbrack)$Out$-1$

About

Examples	2

See also: IncidenceAlgebra, PosetElements, MoebiusFunction