2021/02/25 by Bonato, Anthony, Huggan, Melissa A., Nowakowski, Richard J.
#91A46 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.13225
We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by first applying a reduction, then decomposing the position into an iterated ordinal sum. This is unusual since moves in the middle of the line do not eliminate the rest of the line. Moreover, when G is decomposed into lines H and K, then G=(H:KR). This is in contrast to Hackenbush Strings where G= (H:K).