On the number of standard and of eective multiple alignments

We study the number of all possible alignments of N sequences, N 2, for two distinct alignment concepts proposed in the literature { standard alignments and eective alignments (consistent equivalence relations). Re-cursion formulae are developed to calculate these numbers. For standard alignments and for eective alignment of just two sequences an explicit formula is also presented. The number of all eective alignments of a given site space is shown to be related to Stirling numbers of second kind.