title: The number of reduced alignments between two DNA sequences.
abstract: 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.
  
  
  METHODS
  Primary 92B05, 33C20, secondary 39A14, 65Q30.
authors.forename: Helena
authors.initials: H
authors.lastname: Andrade
authors.forename: Iván
authors.initials: I
authors.lastname: Area
authors.affiliation: Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain. juanjose.nieto.roig@usc.es.
authors.forename: Juan J
authors.initials: JJ
authors.lastname: Nieto
authors.forename: Angela
authors.initials: A
authors.lastname: Torres
mesh_terms: D001483:Base Sequence; D004247:DNA / Q000737:chemistry* / Q000235:genetics; D016415:Sequence Alignment; D017422:Sequence Analysis, DNA / Q000379:methods*; D012984:Software
chemical_list: D004247:DNA