node package manager
Share your code. npm Orgs help your team discover, share, and reuse code. Create a free org »




Combinatorics.js is a standalone math library for Javascript and Node.js. It features a solution to work with Permutations, Posets, Trees, and other enumerative collections.

Combinatorics.js is also a module to math.js.

Please see this blog article to get a general feel for this project.

Table of Contents

  1. Install/Build
  2. Roadmap
  3. Contributing
  4. License


To clone this project:

git clone
cd combinatorics.js

To install the necessary dependencies:

npm install

To test we use Mocha:

npm test // mocha test --recursive

To build we use Gulp:



A rough roadmap for Combinatorics.js

Permutation: π : {1...m} -> {1...m}:

  • Behaviors
    • Inverse
    • Multiply
    • Calculate number of cycles
    • Complement
    • Reverse
    • Randomize Permutation
  • States
    • Number of cycles
    • Parity (odd/even)
    • Number of fixed points (is it a Derangement?)
    • Is Identity
  • Ancillary
    • Create/Return iterator
    • Print to cycle notation

Util Functions

  • Is Integer
  • Combinations
  • Enumerative Methods
    • Bell Numbers
    • Stirling numbers of the first kind
    • Partitions
      • (Weak) Compositions
      • Set Partitions
        • Stirling numbers of the second kind
      • Integer Paritions


Feel free to contribute to combinatorics.js! You can contribute in different ways: spread the word, report bugs, come up with ideas and suggestions, and contribute to the code.

There are a few preferences regarding code contributions:

Combinatorics.js follows the node.js code style
Send pull requests to the develop branch, not the master branch.
Pleae do not commit any files other than in lib/ and test/.
If adding functionality, please include source (lib/) and test (test/) files.


Adapted from math.js


Copyright (C) 2015 Devan Patel

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.