Misère-play Hackenbush Sprigs

Details Misère-play Hackenbush Sprigs Misère-play Hackenbush Sprigs

2012-02-25

arxiv.org/abs/1202.5654v1

Mathematics

Combinatorics

13 pages, 2 figures (1 in color)

Scientific paper

A Hackenbush Sprig is a Hackenbush String with the ground edge colored green and the remaining edges either red or blue. We show that in canonical form a Sprig is a star-based number (the ordinal sum of star and a dyadic rational) in mis\`ere-play, as well as in normal-play. We find the outcome of a disjunctive sum of Sprigs in mis\`ere-play and show that it is the same as the outcome of that sum plus star in normal-play. Along the way it is shown that the sum of a Sprig and its negative is equivalent to 0 in the universe of mis\`ere-play dicotic games, answering a question of Allen.

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