Isoperimetric theorems in the binary sequences of finite lengths Original Research Article

We solve the isoperimetric problem for subsets in the set χ∗ of binary sequences of finite length for two cases: 1. (1) the distance counting the minimal number of insertions and deletions transforming one sequence into another; 2. (2) the distance, where in addition also exchanges of letters are allowed. In the earlier work, the range of the competing subsets was limited to the sequences χn of length n.