N. Terekhov

activity

20242026

collaborators

6 papers

math.CO2026

The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square

Turgay Akyar, Artem Beliakov, Konstantin Delchev +6

Place one grain at every nonsink vertex of the wired $n \times n$ square, and let $L (n)$ be the order of this operation in the sandpile group. Thus $L (n)$ is the least positive $q$ …

math.CO2026

Weak saturation of tensor product of cliques

Nikolai Terekhov

Given two hypergraphs $G$ and $H$ , the weak saturation number $wsat (G, H)$ is the minimum number of edges in a spanning subhypergraph $F$ of $G$ such that th…

math.CO2026

Asymptotically optimal lower bounds on weak saturation numbers for hypergraphs

Nikolai Terekhov

Given an $r$ -uniform hypergraph $H$ and a positive integer $n$ , the weak saturation number $wsat (n, H)$ is the minimum number of edges in an $r$ -uniform hypergraph $F$ on $…

math.CO2026

Forbidding just one intersection for short integer sequences

Elizaveta Iarovikova, Fedor Noskov, Georgy Sokolov +1

In this paper, we study the famous Erdős--Sós forbidden intersection problem for words over an alphabet of size $m$ : what is the maximal size of a subfamily $F$ of $[m]^n…

math.CO2025

A short proof of Tuza's conjecture for weak saturation in hypergraphs

Nikolai Terekhov

Given an $r$ -uniform hypergraph $H$ and a positive integer $n$ , the weak saturation number $wsat (n, H)$ is the minimum number of edges in an $r$ -uniform hypergraph $F$ on $…

math.CO2024

Weak saturation rank: a failure of linear algebraic approach to weak saturation

Nikolai Terekhov, Maksim Zhukovskii

Given a graph $F$ and a positive integer $n$ , the weak $F$ -saturation number $wsat (K_{n}, F)$ is the minimum number of edges in a graph $H$ on $n$ vertices such that the edge…