CDL: A fast and flexible library for the study of permutation sets with structural restrictions

TL;DR

CDL is a versatile software library that efficiently analyzes permutation sets with structural restrictions, supporting pattern avoidance and other conditions relevant in combinatorics, computer science, and social choice.

Contribution

It introduces a flexible, fast library with multiple search strategies for studying restricted permutation sets, including isomorphism detection and large domain exploration.

Findings

Supports pattern avoidance and 'never conditions' analysis

Includes multiple search heuristics for large sets

Enables isomorphism testing of permutation sets

Abstract

In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of interest in both computer science and combinatorics, and "never conditions" utilized in social choice and voting theory. CDL offers a range of fundamental functionalities, including identifying the permutations that meet specific restrictions and determining the isomorphism of such sets. To facilitate exploration of large permutation sets or domains, CDL incorporates multiple search strategies and heuristics.