Article ID Journal Published Year Pages File Type
6871178 Discrete Applied Mathematics 2018 7 Pages PDF
Abstract
In an ordinal sum of two combinatorial games G and H, denoted by G:H, a player may move in either G (base) or H (subordinate), with the additional constraint that any move on G completely annihilates the component H. It is well-known that the ordinal sum does not depend on the form of its subordinate, but depends on the form of its base. In this work, we analyze G(G:H) where G and H are impartial forms, observing that the G-values are related to the concept of minimum excluded value of orderk. As a case study, we introduce the ruleset oak, a generalization of green hackenbush. By defining the operation gin sum, it is possible to determine the literal forms of the bases in polynomial time.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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