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arXiv · 2509.03390

Row Impartial Terminus

Eric Gottlieb·Dawood Khatana·Matjaž Krnc·Peter Muršič·Ismael Qureshi
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Abstract

We introduce Row Impartial Terminus (RIT), an impartial combinatorial game played on integer partitions. We show that any position in RIT can be uniquely decomposed into a core and a remnant. Our central result is that the Conway pair of any RIT position-which determines the outcome under both normal and mis\`ere play-is identical to the Conway pair of a corresponding position in the game of Nim defined by the remnant. This finding provides a complete winning strategy for both variants of RIT, reducing its analysis to the well-understood framework of Nim. As a consequence, we classify RIT within the Conway-Gurvich-Ho hierarchy, showing it to be forced and miserable but not pet.

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Eric Gottlieb, Dawood Khatana, Matjaž Krnc, Peter Muršič, Ismael Qureshi. 2025-09-03. Row Impartial Terminus. https://arxiv.org/abs/2509.03390

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