Diametric theorems in sequence spaces

Abstract

We determine in almost all Manhattan lattices configurations, which for specified diameter have maximal cardinality. Cases, in which those configurations are spheres, have been studied recently by Kleitman and Fellows.

For Hamming spaces we present a partial result supplementing a result of Frankl and Füredi and we formulate a general conjecture.

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Ahlswede, R., Cai, N. & Zhang, Z. Diametric theorems in sequence spaces. Combinatorica 12, 1–17 (1992). https://doi.org/10.1007/BF01191200

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AMS subject classification (1991)

  • 05 A 20
  • 52 C 17
  • 05 D 05