Counting Suffix Arrays and Strings

Suffix arrays are used in various application and research areas like data compression or computational biology. In this work, our goal is to characterize the combinatorial properties of suffix arrays and their enumeration. For fixed alphabet size and string length we count the number of strings sharing the same suffix array and the number of such suffix arrays. Our methods have applications to succinct suffix arrays and build the foundation for the efficient generation of appropriate test data sets for suffix array based algorithms. We also show that summing up the strings for all suffix arrays builds a particular instance for some summation identities of Eulerian numbers.