Speciication of All Maximal Subsets of the Hamming Space with Respect to given Diameter
نویسنده
چکیده
We described here all the maximal-sized subsets of the n-cube B n with respect to given diameter and showed the connection between this description and the discrete isoperimetric problem. As a consequence for any number m, 1 m 2 n , the m-element subset of B n with minimal possible diameter was found. Except of it we present here as a second consequence the simple proof of the Theorem of Katona about intersecting families 4].
منابع مشابه
Specification of all Maximal Subsets of the Hamming Space with Respect to Given Diameter
We present a specification of all maximum subsets of the n-cube Bn with respect to a given diameter and show relations between this problem and the discrete isoperimetric problem. As a corollary, for any number m, 1 ≤ m ≤ 2n, we specify an m-element subset of Bn with minimal possible diameter. We also present a simple proof for a theorem of Katona on intersecting families [4].
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