On Existence of a Regular Hypersimplex Inscribed into the (4n - 1)-Dimensional Cube - Medianik, A. I. (Журнал математичної фізики, аналізу, геометрії, 2006)
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 y_0,y_0’,y_1,y_1’,…, y_2n-2,y_2n-2’ has at least one solution with a real value of y_0 or any other y_i eq 0, i1. Mathematics Subject Classification: 05B20, 52B.