Discovering a new universal partizan ruleset

TL;DR

This paper introduces a new ruleset called turning tiles in combinatorial game theory, proving it is universal for all partizan game positions, expanding understanding of game universality.

Contribution

The paper presents the turning tiles ruleset and proves it is a universal partizan ruleset, allowing all combinatorial game positions to be represented.

Findings

Turning tiles ruleset is universal for all partizan game positions.

It is the second known universal partizan ruleset after generalized konane.

The ruleset enables comprehensive representation of combinatorial game elements.

Abstract

In Combinatorial Game Theory, we study the set of games G, whose elements are mapped from positions of rulesets. In many case, given a ruleset, not all elements of G can be given as a position in the ruleset. It is an intriguing question what kind of ruleset would allow all of them to appear. In this paper, we introduce a ruleset named turning tiles and prove the ruleset is a universal partizan ruleset, that is, every element in G can occur as a position in the ruleset. This is the second universal partizan ruleset after generalized konane.