@enumeratio/incidence

Incidence-algebra extensions for compute-engine: finite posets, the zeta and Möbius functions, and Möbius inversion. The algebra's basis is indexed by a poset's intervals, and the product is composition — composable intervals compose, everything else annihilates. That makes it the first family in this section whose product is usually zero. See the guide.

Declaring

import { ComputeEngine } from "@cortex-js/compute-engine";
import { declareIncidence } from "@enumeratio/incidence";

const ce = new ComputeEngine();
declareIncidence(ce);

Heads

• Posets — Chain, BooleanLattice, DivisorLattice, PosetElements, PosetInterval
• The algebra — IncidenceAlgebra, PosetZeta, PosetSumDown
• Möbius — MoebiusFunction, MoebiusInvert

src/poset.ts also exports the underlying Poset model directly — matrixOf, zeta, moebius, convolve — for computing on posets without going through compute-engine.

Usage

MoebiusFunction(DivisorLattice(30), 1, 30)   // -1 — squarefree, three primes
MoebiusFunction(DivisorLattice(12), 1, 12)   //  0 — 4 divides 12
MoebiusFunction(BooleanLattice(3), [], [1, 2, 3])   // -1 — inclusion–exclusion

Next

The guide's central fact is $ζ * μ = δ$, checked as a matrix identity on every poset here — that identity is what forces $μ$'s recursive definition and what Möbius inversion rests on.

Pages

• Incidence Algebras

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• Source: packages/symbols/algebras/incidence
• Depends on: boxes, engine, structures
• In development, also: config, manifest