Partizan Kayles and Misere Invertibility
Combinatorics
2013-09-09 v1
Abstract
The impartial combinatorial game Kayles is played on a row of pins, with players taking turns removing either a single pin or two adjacent pins. A natural partizan variation is to allow one player to remove only a single pin and the other only a pair of pins. This paper develops a complete solution for "Partizan Kayles" under misere play, including the misere monoid all possible sums of positions, and discusses its significance in the context of misere invertibility: the universe of Partizan Kayles contains a position whose additive inverse is not its negative, and, moreover, this position is an example of a right-win game whose inverse is previous-win.
Keywords
Cite
@article{arxiv.1309.1631,
title = {Partizan Kayles and Misere Invertibility},
author = {Rebecca Milley},
journal= {arXiv preprint arXiv:1309.1631},
year = {2013}
}