3 papers
math.CO2026
On the -positions of some infinite families of Slow -Nim
Silvia Heubach, Matthieu Dufour
We introduce the game Slow -Nim which generalizes a number of recently studied games. Slow -Nim is played on stacks of tokens, and the set indicates the number of sta…
math.CO2026
Necklace Games
Balaji R. Kadam, Silvia Heubach, Matthieu Dufour
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 t…
math.CO2026
The Invariance Reduction Process -- a New Tool to Solve Circular Nim and Related Games
Balaji R. Kadam, Matthieu Dufour, Silvia Heubach
We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge…