On the largest subsets avoiding the diameter of (0, ±1)-vectors

Saori Adachi, Hiroshi Nozaki


Let Lmkl ⊂ Rm + k + l be the set of vectors which have m of entries  − 1, k of entries 0, and l of entries 1. In this paper, we investigate the largest subset of Lmkl whose diameter is smaller than that of Lmkl. The largest subsets for m = 1, l = 2, and any k will be classified. From this result, we can classify the largest 4-distance sets containing the Euclidean representation of the Johnson scheme J(9, 4). This was an open problem in Bannai, Sato, and Shigezumi (2012).


The Erdős-Ko-Rado theorem, s-distance set, diameter graph, independent set, extremal set theory

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ISSN: 1855-3974

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