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

  • 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

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.

Ключові слова:

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

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Як цитувати

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

Номер

Том 2 № 1 (2006)

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