On the combinatorics of suffix arrays

TL;DR

This paper explores the combinatorial structure of suffix arrays, establishing a new characterization via permutations and linking it to Burrows-Wheeler arrays, thereby simplifying proofs and extending understanding of suffix array properties.

Contribution

It introduces a novel permutation-based characterization of suffix arrays, connecting them with Burrows-Wheeler arrays and simplifying enumeration proofs.

Findings

Characterization of suffix arrays through permutations.

Connection between suffix arrays and Burrows-Wheeler arrays.

Simplified proofs for enumeration results.

Abstract

We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays given in [1], that we apply by reducing suffix sorting to cyclic shift sorting through the use of an additional sentinel symbol. We show that the characterization of suffix arrays for a special case of binary alphabet given in [2] easily follows from our characterization. Based on our results, we also provide simple proofs for the enumeration results for suffix arrays, obtained in [3]. Our approach to characterizing suffix arrays is the first that exploits their relationship with Burrows-Wheeler permutations.