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schur-partition-search

Run simulated-annealing searches for Schur partition problems from algebraic seeds.

1|Updated Mar 14, 2026
Search Tags:#optimization#combinatorics#coloring#simulated-annealing#partition#schur#algebraic-seed
One-click install
npx skills add https://github.com/bneb/perqed --skill schur-partition-search
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: schur-partition-search
Source: https://github.com/bneb/perqed/tree/main/.agents/skills/schur-partition-search
Command: npx skills add https://github.com/bneb/perqed --skill schur-partition-search

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Schur-partition-search tackles combinatorial optimization problems in Schur partitioning by applying a simulated-annealing (SA) optimizer seeded from algebraic partitions, enabling exploration beyond algebraic seeds to find valid witnesses when E > 0.

Core Features & Use Cases

  • Warm-started SA from algebraic seeds for improved convergence on Schur-partition problems.
  • Flexible configuration for domain_size, number_partitions, and sa_iterations, with optional warm_start_from_node chaining.
  • Returns the best partition found and records the associated energy E, signaling a valid witness when E=0.

Quick Start

Run a partition_sa_search with domain_size 537, num_partitions 6, sa_iterations 5000000, starting from a prior algebraic_partition_construction seed.

Frequently Asked Questions about schur-partition-search

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I find a valid Schur partition when my algebraic seed leaves energy greater than zero?▼

Schur partition search applies a simulated-annealing optimizer seeded from algebraic partitions to explore beyond the initial seed and find valid sum-free coloring witnesses when energy E is greater than zero.

What inputs do I need to run a Schur-number partition experiment?▼

You need to provide domain_size, num_partitions, and sa_iterations. Optionally, you can use warm_start_from_node to chain searches from a prior algebraic partition construction seed.

Can I chain multiple simulated-annealing searches for combinatorial optimization?▼

Yes, you can chain searches by setting the warm_start_from_node parameter to the output of a prior algebraic partition construction, allowing the simulated-annealing optimizer to continue from a previous state.

How do I know if a sum-free coloring task has a valid witness?▼

The search returns the best partition found and records its energy E. A valid witness for the sum-free coloring task is confirmed when the output energy E equals zero.

What are the limitations of using simulated annealing for Schur partition problems?▼

The simulated-annealing approach relies on algebraic seeds to warm-start, meaning it requires an existing partition to seed from and sufficient sa_iterations to converge, making it dependent on prior algebraic construction.

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