What mathematical structures does this skill support?

It supports positive integers (divisors), locally finite posets (partially ordered sets), lattices such as bond lattices, and incidence algebras.

Does it include database schema support?

Yes, the skill includes DuckDB schema definitions for persistent storage of Möbius values, poset relations, and chromatic coefficients.

What is the significance of GF(3) in this context?

It utilizes the Möbius value μ(3) = -1 as a fundamental sign flip to establish action-perception duality in bidirectional computational systems.

How does it handle graph theory problems?

The skill calculates chromatic polynomials using Whitney's formula and validates node centrality through alternating Möbius-weighted sums.

Is this skill compatible with the Julia scientific ecosystem?

Yes, it provides specific implementation patterns for Julia packages including Primes.jl, Graphs.jl, Catlab.jl, and AbstractAlgebra.jl.

Möbius Inversion Engine

Name: Möbius Inversion Engine
Author: plurigrid

byplurigrid

•

데이터 과학 및 ML

Performs advanced Möbius inversion on partially ordered sets and lattices to solve complex combinatorial, topological, and graph-theoretic problems.

The Möbius Inversion skill provides a specialized framework for calculating the Möbius function across various mathematical structures, facilitating the recovery of local data from global cumulative sums. It enables developers and researchers to handle incidence algebras, generate chromatic polynomials via bond lattices, and validate network centrality using alternating sums. Specifically designed for topological computation, this skill integrates patterns for Julia scientific computing and bidirectional systems, making it essential for projects involving discrete mathematics, category theory, and the GF(3) trit system.

주요 기능

01Integration with GF(3) sign-inversion symmetry for topological modeling

02Centrality validation using local-global inversion patterns

032 GitHub stars

04Implementation of incidence algebras and convolution products

05Poset and lattice-based Möbius function calculation

06Generation of chromatic polynomials via bond lattices

사용 사례

01Implementing bidirectional mathematical logic in Julia scientific workflows

02Analyzing local node contributions within global network centrality models

03Computing proper graph colorings and chromatic coefficients for network analysis

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi moebius-inversion

For use in Claude.ai and ChatGPT

Download Skill