On plateaued Boolean functions with the same spectrum support

In the first half of the paper we give a brief review of plateaued functions, regular functions and related topics including connections with problems on subgraphs of the Hamming graph. In the second half of the paper we discover wide infinite families of spectrum supports for which it is possible to count the number of plateaued Boolean functions with such spectrum supports and give corresponding formulas; only one infinite sequence of such spectrum supports was known before.