Title：On equitable partitions with long life

Speaker：Denis Krotov (Sobolev Institute of Mathematics)

Time：Aug. 25, 4：30 p.m. - 5：30 p.m.

Place：2104

Abstract：For the Hamming graph $H(n,q)$, where $q$ is constant and $n$ grows, we construct perfect colorings (equitable partitions) without non-essential arguments such that $n$ depends exponentially on the off-diagonal part of the quotient matrix. In particular, we construct unbalanced Boolean functions such that the number of essential arguments depends exponentially on the degree of the function. (Joint work with Alexandr Valyuzhenich)