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

11/02/2015

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by   Steffen Eger, et al.

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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={(s_1,...,s_N) | 1< s_i< 2}.