The Structure of the Distributive Lattice of Games Born by Day n

We prove structural theorems about the distributive lattice of games born by day n. For instance, the number of join-irreducible elements is exactly twice the number of elements born by day n − 1. As an immediate corollary, all maximal chains on day n are of length exactly one plus double the number of born by day n − 1.

Related Organizations

University of California, Berkeley
United States
Gustavus Adolphus College
United States

Keywords

Combinatorial games

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