A Sperner labeling of the regular triangulation of the integer simplex Δ_{k,q} has between binomial(q+k-3,k-2) and q^(k-1)-(q-1)^(k-1) non-monochromatic cells.
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On the minimum number of non-monochromatic simplices for Sperner labelings of a regular triangulation
A Sperner labeling of the regular triangulation of the integer simplex Δ_{k,q} has between binomial(q+k-3,k-2) and q^(k-1)-(q-1)^(k-1) non-monochromatic cells.