V. Gurvich

activity

20232026

most citedGM-rule and its applications to impartial games

3 citations · 4 across the 10 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.CO2026

Bridge distances for networks

Vladimir Gurvich, Mariya Naumova

Let $G = (V, E)$ be a finite directed graph with a non-negative real length $μ_{e}$ assigned to every directed edge $e \in E$ . We assume that $μ_{e} = + \infty$ for every non-edge $e \no…

math.CO2025

Partitioning set $[n] = {1, \dots, n}$ into subsets of size at most $m$ such that all sums are powers of $m$

Vladimir Gurvich, Mariya Naumova

Given integers $m > 1$ and $n > 0$ , we say that a partition of the set $[n] = {1, \dots, n}$ is {\em $m$ -good} if the number of elements in each part is at most $m$ and their sum…

math.CO2024

A counterexample to conjecture "Catch 22"

Bogdan Butyrin, Vladimir Gurvich, Anton Lutsenko +2

We construct a finite deterministic graphical (DG) game without Nash equilibria in pure stationary strategies. This game has 3 players $I = {1, 2, 3}$ and 5 outcomes: 2 terminal $a_1…

math.CO2024

Growing Trees and Amoebas' Replications

Vladimir Gurvich, Matjaž Krnc, Mikhail Vyalyi

An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length $ℓ$ . This paper analyses such a growth process. An amoeba is morta…

math.CO2023

Screw discrete dynamical systems and their applications to exact slow NIM

Vladimir Gurvich, Mariya Naumova

Given integers $n, k, ℓ$ such that $0 < k < n, 1 < ℓ$ and an integer vector $x = (x_{1}, \dots, x_{n})$ ; denote by $m = m (x)$ the number of entries of $x$ that are multiple of $ℓ$ .…

math.CO2023★ 1 cited

Experimental Study of the Game Exact Nim(5, 2)

Vladimir Gurvich, Artem Parfenov, Michael Vyalyi

We compare to different extensions of the ancient game of nim: Moore's nim $(n, \leq k)$ and exact nim $(n, = k)$ . Given integers $n$ and $k$ such that $0 < k \leq n$ , we consider $n…

math.CO2023

On remoteness functions of k-NIM with k+1 piles in normal and in misère versions

Vladimir Gurvich, Vladislav Maximchuk, Georgy Miheenkov +1

Given integer $n$ and $k$ such that $0 < k \leq n$ and $n$ piles of stones, two players alternate turns. By one move it is allowed to choose any $k$ piles and remove exactly one st…

math.CO2023★ 3 cited

GM-rule and its applications to impartial games

Vladimir Gurvich, Mariya Naumova

Given integer $n \geq 1, ℓ \geq 2$ , and vector $x = (x_{1}, \dots, x_{n})$ that has an entry which is a multiple of $ℓ$ and such that $x_{1} \leq \dots \leq x_{n}$ , the GM-rule is…

Bridge distances for networks

Partitioning set [n]={1,…,n} into subsets of size at most m such that all sums are powers of m

A counterexample to conjecture "Catch 22"

Growing Trees and Amoebas' Replications

Screw discrete dynamical systems and their applications to exact slow NIM

Experimental Study of the Game Exact Nim(5, 2)

On remoteness functions of k-NIM with k+1 piles in normal and in misère versions

GM-rule and its applications to impartial games

Partitioning set $[n] = {1, \dots, n}$ into subsets of size at most $m$ such that all sums are powers of $m$