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math.CO2025
-Ending partisan rulesets
Hiroki Inazu, Shun-ichi Kimura, Koki Suetsugu
In this paper, we consider -ending partisan rulesets as a branch of combinatorial game theory. In these rulesets, the sets of options of both players are th…
math.CO2025
Digraph Yama Nim
Hiyu Inoue, Shun-ichi Kimura, Hikaru Manabe +3
{\sc Yama Nim} is a variant of two piles {\sc Nim}. In this ruleset, the player chosses one of the piles and removes at least two tokens from the pile. In the same move, the player…
math.CO2025
Combinatorial Games and the Golden Ratio on Digraphs
Tomoaki Abuku, Hiroki Inazu, Hiyu Inoue +4
We introduce a new combinatorial game called Triangle Game. In this game, a directed -cycle graph is given, and stones are placed on each vertex. The player chooses a directed e…