Ordinal sums, clockwise hackenbush, and domino shave
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski, Carlos Pereira dos Santos · 2022
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 bluered hackenbush 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 hackenbush.