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On a discrete version of the antipodal theorem

Krzysztof Oleszkiewicz (1996)

Fundamenta Mathematicae

The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping there exists a point such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of which were previously known (as far as the author knows) only for f linear (cf. [1]).

On 's and 's admitting a semiregular automorphism group of order 9.

Akiyama, Kenzi, Ogawa, Masayuki, Suetake, Chihiro (2009)

The Electronic Journal of Combinatorics [electronic only]

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