What is the primary use of the Möbius inversion skill?

It is used to invert cumulative sums over partially ordered sets, allowing users to recover local values from global constraints in graph theory and combinatorics.

Can this skill help with graph coloring problems?

Yes, it specifically implements Whitney's formula and bond lattice analysis to calculate chromatic polynomials for determining proper graph colorings.

Is this skill compatible with Julia-based scientific computing?

Yes, the skill includes implementation patterns for integration with Julia packages like Graphs.jl, Primes.jl, and Catlab.jl for advanced scientific modeling.

How does it relate to the GF(3) trit system?

It utilizes the Möbius value of 3 (which is -1) to create the fundamental sign-flip symmetry required for modeling action-perception dualities in topological systems.

Möbius Inversion & Poset Analysis

Name: Möbius Inversion & Poset Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Calculates Möbius functions and alternating sums on posets to solve complex combinatorial, graph theory, and network centrality problems.

The moebius-inversion skill provides Claude with advanced mathematical capabilities for analyzing partially ordered sets (posets) and lattices. It enables the inversion of cumulative sums to recover local data from global structures, a fundamental technique in combinatorial theory and network analysis. Users can leverage this skill to compute chromatic polynomials via bond lattices, manage incidence algebras, and implement bidirectional computation patterns. It is especially powerful for developers and researchers working with topological data structures, GF(3) trit systems, and scientific modeling in Julia.

Key Features

01Performs inversion on locally finite posets and lattice structures

02Implements incidence algebra operations including convolution products

03Validates network centrality metrics via alternating harmonic path sums

048 GitHub stars

05Computes number-theoretic Möbius functions and Euler's totient values

06Generates chromatic polynomials for graphs using Whitney’s formula

Use Cases

01Analyzing graph connectivity and proper k-colorings in network design

02Implementing sign-inversion logic and perception-action dualities in GF(3) systems

03Validating local-global consistency in complex topological and categorical data structures

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