moebius-inversion
Möbius inversion on posets and lattices: alternating sums, chromatic polynomials, incidence algebras, and centrality predicates.
npx skills add majiayu000/claude-skill-registry --skill moebius-inversion --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Möbius Inversion Skill > *"The Möbius function inverts summation over divisors - the fundamental tool connecting local constraints to global structure."* ## bmorphism Contributions > *"all is bidirectional"* > — [@bmorphism](https://gist.github.com/bmorphism/ead83aec97dab7f581d49ddcb34a46d4), Play/Coplay gist **Categorical Connection**: Möbius inversion on posets is the prototypical example of **adjunction** in category theory — ζ and μ form a zeta-Möbius pair where convolution is the composition operation. This connects to: - **Incidence algebras** as categorical structures on posets - **Bidirectional computation** — inversion recovers local from global - **Chromatic polynomials** via ACSet bond lattices **Plurigrid Integration**: The GF(3) trit system uses μ(3) = -1 (3 is prime) as the fundamental sign flip that creates the action-perception duality: - Action trits: {-, 0, +} - Perception trits: {+, 0, -} (Möbius-inverted) - Double inversion: μ ∘ μ = identity **Key Reference**: - Rota (1964) — "On the Foundations of Combinatorial Theory I: Theory of Möbius Functions" ## Overview Möbius inversion provides: 1. **Alternating sums** - Invert cumulative sums to get point values 2. *
- bmorphism Contributions
- Overview
- Classical Möbius Function
- Definition
- Key Values
- Implementation
- Möbius Inversion Formula
- For Divisors
- Example: Euler's Totient
- Möbius on Posets
- General Definition
- Inversion on Posets
- Chromatic Polynomial
- Bond Lattice
just moebius-table 100 # Print μ(n) for n ≤ 100 just moebius-invert data.json # Apply inversion to sums just moebius-chromatic graph.json 5 # P(G, 5) just moebius-centrality graph.json # Alternating harmonic centrality just moebius-verify graph.json # Validate centrality predicates
What does the moebius-inversion skill do?
Möbius inversion on posets and lattices: alternating sums, chromatic polynomials, incidence algebras, and centrality predicates.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill moebius-inversion --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.