Various Diamond Properties in Combinatorial Game Theory
Abstract
We investigate conditions under which positions in combinatorial games admit simple values. We introduce a unified diamond framework, the ◇A-property (A ∈ {ℤ, 𝔻}), for sets of positions closed under options. Under certain conditions, this framework guarantees that all values are integers, dyadic rationals, or pairs {m | n} (on ℤ or 𝔻). As an application, we establish that every position in Yashima game on bipartite graphs has an integer pair value.
Fields of Study & Subjects
Artificial Intelligence in Games
Limits and Structures in Graph Theory
Advanced Graph Theory Research
Publication details
- Journal / source
- IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
- Publication date
- 1 January 2026
- Language
- EN