Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)
Chapter: Alignment Given
Page 95
or
where in the first case there are three identities, two substitutions, and one insertion/deletion (indel) and in the second case there are two identities, three substitutions, and one indel.
An alignment can be obtained by inserting gaps ("-") into the sequences so that
and
Here the subsequence of all 
is identical to A1A2. . . An. Then, since the *-sequences have equal length, 
is aligned with 
. In Chapter 3, algorithms to achieve optimal alignments are discussed. Here we are interested in the statistical distribution of these scores, not in how they are obtained. Global alignments refer to the situation where all the letters of each sequence must be accounted for in the alignments. There are two types of global alignments, alignments where the pairing is given and alignments where the pairing is not given.
Alignment Given
In this section, we assume the alignment is given with the sequences:
A1A2. . . An
B1B2. . . Bn
(Gaps "" have been added so that these sequences both have the same lengthL in the previous section, n hereand the stars have been omitted to simplify the notation.) In this case the alignment is given and
