Software for enumerative and analytic combinatorics

TL;DR

This paper surveys various freely available symbolic software packages that implement algorithms from enumerative and analytic combinatorics, covering their capabilities, algorithms, and applications.

Contribution

It provides a comprehensive overview of existing software tools for combinatorics, highlighting their features and underlying algorithms.

Findings

Most packages are freely downloadable from the web.

Software covers areas like basic objects, symbolic combinatorics, Pólya theory, and asymptotics.

Descriptions include capabilities and references to documentation.

Abstract

We survey some general-purpose symbolic software packages that implement algorithms from enumerative and analytic combinatorics. Software for the following areas is covered: basic combinatorial objects, symbolic combinatorics, P\'olya theory, combinatorial species, and asymptotics. We describe the capabilities that the packages offer as well as some of the algorithms used, and provide links to original documentation. Most of the packages are freely downloadable from the web.