The number of reduced alignments between two DNA sequences

Background: In this study we consider DNA sequences as mathematical strings. Total and reduced alignments between two DNA sequences have been considered in the literature to measure their similarity. Results for explicit representations of some alignments have been already obtained. Results: We present exact, explicit and computable formulas for the number of different possible alignments between two DNA sequences and a new formula for a class of reduced alignments. Conclusions: A unified approach for a wide class of alignments between two DNA sequences has been provided. The formula is computable and, if complemented by software development, will provide a deeper insight into the theory of sequence alignment and give rise to new comparison methods.AMS Subject Classification: Primary 92B05, 33C20, secondary 39A14, 65Q30. © 2014 Andrade et al.; licensee BioMed Central Ltd.