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math.CO2025
Cyclic impartial games with carry-on moves
Tomoaki Abuku, Alda Carvalho, Urban Larsson +3
In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial g…
math.CO2021
A Note on Numbers
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage t…
math.CO2020
Ordinal Sums, Clockwise Hackenbush, and Domino Shave
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
We present two rulesets, Domino Shave and Clockwise Hackenbush. The first is somehow natural and, as special cases, includes Stirling Shave and Hetyei's Bernoulli game. Clockwise H…