Counts distinct necklaces and bracelets using Burnside's lemma from length and color count to solve combinatorial symmetry counting problems.
Count distinct necklaces and bracelets using Burnside's lemma.
| Name | Required | Description | Default |
|---|---|---|---|
| k | Yes | Number of colors (1-1000) | |
| n | Yes | Length (1-1000) |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare the operation read-only, idempotent, open-world, and non-destructive, so the description does not need to cover safety. It adds the Burnside's lemma method but says nothing about return shape, edge cases, or computational limits; with annotations present this is adequate but thin.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
It is a single front-loaded sentence with no filler or repetition. The terseness is appropriate for a simple two-parameter math tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Because there is no output schema, the description should clarify whether the result is one count or separate necklace/bracelet counts, and what the return value represents. It also leaves the rotation-vs-reflection distinction implicit, which is a meaningful gap for Burnside's lemma applications.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%, and the schema already defines n as length and k as number of colors with valid ranges. The description adds no parameter semantics beyond those field descriptions, so the baseline 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description pairs the specific verb "Count" with the specific combinatorial objects "distinct necklaces and bracelets" and names the method (Burnside's lemma). This clearly distinguishes it from the surrounding math and utility siblings, none of which perform necklace/bracelet enumeration.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no explicit when-to-use, when-not-to-use, or alternative guidance. The agent must infer from the specialized phrase that this applies to circular arrangements with n positions and k colors; no prerequisites or boundaries are stated.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.