Necklace Games
Combinatorics
2026-04-14 v1
Abstract
We define and give results on the game NecklaceNim NN(,) which is PathNim PN(,) with an additional move allowed on the end vertices. This game arises as a sub-game in the context of solving CircularNim CN(,) when consecutive stacks have been depleted, therefore its solution is critical to solving CircularNim. We solve the infinite families of NN(,) when play is allowed on at least half the stacks.
Cite
@article{arxiv.2604.10364,
title = {Necklace Games},
author = {Balaji R. Kadam and Silvia Heubach and Matthieu Dufour},
journal= {arXiv preprint arXiv:2604.10364},
year = {2026}
}