Scoring Play Combinatorial Games Under Different Operators

TL;DR

This paper explores scoring play combinatorial games under three different operators—conjunctive sum, selective sum, and sequential join—highlighting their structural properties and differences from normal play games.

Contribution

It introduces analysis of scoring play games under three operators, expanding understanding beyond the disjunctive sum studied previously.

Findings

Scoring play games are partially ordered under disjunctive sum.

Different operators exhibit distinct structural properties.

The paper extends the theoretical framework for scoring play games.

Abstract

Scoring play games were first studied by Fraser Stewart for his PhD thesis. He showed that under the disjunctive sum, scoring play games are partially ordered, but do not have the same "nice" structure of normal play games. In this paper I will be considering scoring play games under three different operators given by John Conway and William Stromquist and David Ullman, namely the conjunctive sum, selective sum and sequential join.