M\"untz spaces and Remez inequalities

Two relatively long-standing conjectures concerning M\"untz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense M\"untz spaces.Comment: 5 page

On monochromatic triangles

AbstractLet A and B be two disjoint finite sets in R2. Simple conditions that guarantee the existence of a triangle with vertices in one of the sets and with no points from the other set in its interior are given. The analogous problem for d-simplices in Rd is treated. Conditions are derived that guarantee the existence of a triangle with vertices in one of the sets and with no points from either set on its boundary