Strictly monotonic multidimensional sequences and stable sets in pillage games

David Saxton

Let $S\subset {\mathbb{R}}^n$ have size $|S|>{\ell }^{2^n-1}$. We show that there are distinct points $\{x^1,...,x^{\ell +1}\}\subset S$ such that for each $i\in [n]$, the coordina…