MoebiusInvert

Möbius inversion: given , recover . The inverse of PosetSumDown, and the reason the incidence algebra is worth having.

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MoebiusInvert(poset, values)

PosetSumDown(poset, values)the map it undoes,

Domain: Incidence algebras

Details

Values are given in the poset's own order — see PosetElements for that listing
On a chain this is first differences; on the Boolean lattice it is inclusion–exclusion; on the divisor lattice it is classical Möbius inversion
The two directions are inverse on every poset, which is the theorem

Examples

See also: MoebiusFunction, PosetElements