PosetSumDown

Sum a function down the poset's order: $g(y) = \sum_{x \le y} f(x)$, the map MoebiusInvert undoes.

PosetSumDown(poset, values)$g(y) = \sum_{x \le y} f(x)$

Typed signatures

Type	Package	Applies
(expression<BooleanLattice> | expression<Chain> | expression<DivisorLattice>, list<number>) -> list<number>	incidence	always

Domain: Incidence algebras

Examples

Basic #

Running totals

live ↗

In$\mathrm{PosetSumDown}(\mathrm{Chain}(4), \bigl\lbrack1, 1, 1, 1\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3, 4\bigr\rbrack$

Subsets counted below each point

live ↗

In$\mathrm{PosetSumDown}(\mathrm{BooleanLattice}(2), \bigl\lbrack1, 1, 1, 1\bigr\rbrack)$Out$\bigl\lbrack1, 2, 2, 4\bigr\rbrack$

About

Examples	2

See also: MoebiusInvert, MoebiusFunction, PosetElements