Alexandr Valyuzhenich

activity

20232026

collaborators

3 papers

math.CO2026

An upper bound on the number of relevant variables in a bounded degree Boolean function on the Hamming graph

Alexandr Valyuzhenich

In this work, we prove that any Boolean function of degree $d$ on $Z_{q}^{n}$ , $q \geq 3$ , has at most $m_{q} q^{d}$ relevant variables, where $m_{q} = \frac{2 q ( q ^{2} + 4 q + 1 )}{( q - 1 ) ^{4}}$ .…

math.CO2025

On $P$ -crucial square-free permutations

Alexandr Valyuzhenich

A permutation is square-free if it does not contain two consecutive factors of length two or more that are order-isomorphic. A square-free permutation of length $n$ is $P$ -crucial,…

math.CO2023

On degree- $3$ and $(n - 4)$ -correlation-immune perfect colorings of $n$ -cubes

Denis S. Krotov, Alexandr A. Valyuzhenich

A perfect $k$ -coloring of the Boolean hypercube $Q_{n}$ is a function from the set of binary words of length $n$ onto a $k$ -set of colors such that for any colors $i$ and $j$ every w…

An upper bound on the number of relevant variables in a bounded degree Boolean function on the Hamming graph

On P-crucial square-free permutations

On degree-3 and (n−4)-correlation-immune perfect colorings of n-cubes

On $P$ -crucial square-free permutations

On degree- $3$ and $(n - 4)$ -correlation-immune perfect colorings of $n$ -cubes