On Existence of a Regular Hypersimplex Inscribed into the (4n - 1)-Dimensional Cube

Abstract

It is proved the existence of a regular hypersimplex inscribed into the (4n-1)-dimensional cube under condition that some system of 4n-2 algebraic equations with 4n-2 unknown quantities y0, y'0, y1; y'1,..., y2n-2, y'2n-2 has at least one solution with a real value of y0 or any other yi ≠ 0, i ≥ 1.