Does this skill support graph theory applications?

Yes, it specifically provides tools for calculating chromatic polynomials via bond lattices and deletion-contraction methods to determine proper graph colorings.

Can I use this for network centrality?

Absolutely, it includes an alternating harmonic centrality algorithm that uses Möbius-weighted paths to determine node importance in a graph.

How does it relate to GF(3) and ternary logic?

The skill integrates with GF(3) systems by treating Möbius inversion as a duality between perception and action, where μ(3) = -1 acts as a central inversion constant.

What mathematical structures does it handle?

It handles number-theoretic divisors, general locally finite posets, bond lattices, and incidence algebras with support for convolutional products.

What is the primary use of the Möbius inversion skill?

It is used to invert cumulative sums over partially ordered sets (posets) to find point values, which is essential for graph coloring, number theory, and network analysis.

Möbius Inversion & Combinatorics

Name: Möbius Inversion & Combinatorics
Author: plurigrid

byplurigrid

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Data Science & ML

Implements Möbius inversion on posets and lattices to solve complex combinatorial problems, graph coloring, and centrality analysis.

This skill provides a comprehensive toolkit for Möbius inversion, bridging the gap between local constraints and global structures in number theory and graph theory. It enables developers to calculate alternating sums, derive chromatic polynomials via bond lattices, and manage incidence algebras. Specifically designed for researchers and engineers working with complex relational data, it includes specialized support for GF(3) (ternary) logic and advanced centrality predicates to validate node importance in topological networks through spectral and combinatorial methods.

Key Features

01Incidence algebra implementation for convolutional products on posets

02Classical Möbius function and Euler's Totient calculations for number theory

03Chromatic polynomial generation using bond lattices and deletion-contraction

04Generalized Möbius inversion on locally finite posets and lattices

057 GitHub stars

06Alternating harmonic centrality measures for advanced network analysis

Use Cases

01Solving inversion problems in number theory and combinatorial optimization

02Calculating the number of proper k-colorings for complex graph structures

03Analyzing node centrality in large-scale topological networks using alternating sums

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