Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill combinatoricsgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/combinatorics)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/combinatorics"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/combinatorics/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/combinatorics"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/combinatorics.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00022 | $0.00214 |
| Opus 5.5 | $0.00009 | $0.00086 |
| Sonnet 5.5 | $0.00004 | $0.00043 |
| Haiku 4.5 | $0.00002 | $0.00021 |
Grade A, and why
combinatorics scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Combinatorics
Domain
Counting and arrangement.
Core Concepts
- Permutations, combinations
- Binomial and multinomial coefficients
- Inclusion–exclusion
- Generating functions
- Partitions, Stirling numbers
Key Methods
- Stars and bars
- Inclusion–exclusion principle
- Recursion + generating functions
- Double counting
Canonical Examples
- C(n,k) = n!/(k!(n-k)!).
- Number of onto functions = inclusion–exclusion.
- Catalan numbers: C_n = (1/(n+1))·C(2n,n).
Common Pitfalls
- Counting ordered vs. unordered
- Overcounting in inclusion–exclusion
- Forgetting empty set / empty arrangement
Related Skills
Discrete Math, Probability, Graph Theory
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 38 lines · 22 tokens per session scan A 8864e9f64b21
combinatorics is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 22 tokens to every session and 214 once invoked, about $0.0001 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-10.
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