Games and Complexes II: Weight Games and Kruskal-Katona Type Bounds

A strong placement game $G$ played on a board $B$ is equivalent to a simplicial complex $Δ_{G,B}$. We look at weight games, a subclass of strong placement games, and introduce upper bounds on the number of positions with $i$ pieces in $G$, or equivalently the number of faces with $i$ vertices in $Δ_{G,B}$, which are reminiscent of the Kruskal-Katona bounds.

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