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

Автор(и)

  • A. I. Medianik B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61103, Ukraine

Ключові слова:

necessary and sufficient conditions, regular simplex, Hadamard's matrix, circulant matrix, antipodal n-gons, generating polinomial, idempotancy

Анотація

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',\ldots, $ $y_{2n-2},y_{2n-2}'$ has at least one solution with a real value of $y_0$ or any other $y_i\neq 0, i\ge 1$.

Mathematics Subject Classification: 05B20, 52B.

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(1)
Medianik, A. I. On Existence of a Regular Hypersimplex Inscribed into the (4n - 1)-Dimensional Cube. Журн. мат. фіз. анал. геом. 2006, 2, 62-72.

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