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 $y_i eq 0, i\ge 1$. Mathematics Subject Classification: 05B20, 52B.