Alexandr Valyuzhenich

collaborators

2 papers

math.CO2026

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

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,…

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 $P$ -crucial square-free permutations