M. Naumova

activity

20212026

most citedGM-rule and its applications to impartial games

3 citations · 4 across the 15 of their papers we have counts for

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Showing math.COShow all

9 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.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

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…

math.CO2023

More on discrete convexity

Vladimir Gurvich, Mariya Naumova

In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a…

math.CO2022★ 1 cited

Lexicographically maximal edges of dual hypergraphs and Nash-solvability of tight game forms

Vladimir Gurvich, Mariya Naumova

Let $A = {A_{1}, \dots, A_{m}}$ and $B = {B_{1}, \dots, B_{n}}$ be a pair of dual multi-hypergraphs on the common ground set $O = {o_{1}, \dots, o_{k}}$ . Note that…

math.CO2021

On Nash-solvability of n-person graphical games under Markov's and a priori realizations

Vladimir Gurvich, Mariya Naumova

We consider graphical $n$ -person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce pr…

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"

Screw discrete dynamical systems and their applications to exact slow NIM

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

GM-rule and its applications to impartial games

More on discrete convexity

Lexicographically maximal edges of dual hypergraphs and Nash-solvability of tight game forms

On Nash-solvability of n-person graphical games under Markov's and a priori realizations

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