On the Number of Many-to-Many Alignments of Multiple Sequences

Abstract

We count the number of alignments of N ≥ 1 sequences when match-up types are from a specified set S ⊆ N N . Equivalently, we count the number of nonnegative integer matrices whose rows sum to a given fixed vector and each of whose columns lie in S. We provide a new asymptotic formula for the case S = {(s1, . . . , sN ) | 1 ≤ si ≤ 2}.