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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…