How does this skill assist with graph coloring?

The skill implements Whitney's formula and bond lattice analysis to compute the chromatic polynomial, which counts the number of ways a graph can be properly colored with k colors.

Can I use this for standard number theory tasks?

Yes, it includes classical implementations for the Möbius function μ(n), Euler's totient function, and divisor-based inversion formulas.

Does it support GF(3) logic systems?

Yes, it specifically integrates with GF(3) systems by leveraging μ(3) = -1 to model perception-action duality and sign-inversion symmetry.

What are incidence algebras in this context?

Incidence algebras are algebraic structures defined over posets that allow you to perform convolutions, effectively managing relationships like summation (zeta function) and its inverse (Möbius function).

What is Möbius inversion used for in this skill?

It is used to invert cumulative sums over partially ordered sets (posets) to determine individual point values, which is critical for solving problems in combinatorics, number theory, and network centrality.

Möbius Inversion & Poset Analysis

Name: Möbius Inversion & Poset Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Implements advanced Möbius inversion on posets and lattices to solve complex combinatorial, graph-theoretic, and number-theoretic problems.

This skill provides a comprehensive suite of tools for applying Möbius inversion across various mathematical domains, including number theory, graph theory, and poset analysis. It enables the computation of chromatic polynomials via bond lattices, the management of incidence algebras, and the validation of node centrality through alternating sums. Specifically designed for researchers and engineers working on topological data analysis and complex network theory, it integrates GF(3) triadic logic to facilitate perception-action duality and spectral validation within the Claude Code environment.

Key Features

01Chromatic polynomial calculation using bond lattices and Whitney’s formula

02Number-theoretic functions for Euler's totient and divisor inversion

03Incidence algebra operations including convolution products and zeta functions

04Centrality predicate validation using local-global inversion techniques

05Generalized Möbius inversion on locally finite posets

067 GitHub stars

Use Cases

01Validating node importance and centrality in complex graphs using alternating sums

02Implementing algebraic structures on partially ordered sets for data modeling

03Calculating graph colorings and chromatic polynomials 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