Isoperimetric problems for r-sets
The Edge isoperimetric inequalities for r-sets was analyzed. A set in the form of a k-ball was discussed. It was observed that to minimize the lower shadow initial segents of the colex order should be taken, and for the upper shadow to be minimized initial segments of the lex order should be taken. It was found that to minimize the number of q-sets at hamming distance from one family it was best to take some balls.
Combinatorics Probability and Computing
Bollobás, B., & Leader, I. (2004). Isoperimetric problems for r-sets. Combinatorics Probability and Computing, 13 (2), 277-279. https://doi.org/10.1017/S0963548304006078