Ordinal sums, clockwise hackenbush and domino shave. (English) Zbl 1490.91029
Summary: We present two rulesets, domino shave and clockwise hackenbush. The first is somehow natural and has, as special cases, stirling shave and Hetyei’s Bernoulli game. Clockwise Hackenbush seems artificial yet it is equivalent to Domino Shave. From the pictorial form of the game, and a knowledge of Hackenbush, the decomposition into ordinal sums is immediate. The values of Clockwise blue-red hackenbusch are numbers and we provide an explicit formula for the ordinal sum of numbers where the literal form of the base is \(\{x|\}\) or \(\{|x\}\), and \(x\) is a number. That formula generalizes van Roode’s signed binary number method for blue-red hackenbusch.
MSC:
| 91A46 | Combinatorial games |
References:
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