Geodesic
On the largest subsets avoiding the diameter of (0, ±1)-vectors
Ars Mathematica Contemporanea, Tome 13 (2017) no. 1, pp. 1-13.

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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).
DOI : 10.26493/1855-3974.935.4e0
Keywords: The Erdős-Ko-Rado theorem, s-distance set, diameter graph, independent set, extremal set theory 
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Saori Adachi; Hiroshi Nozaki. On the largest subsets avoiding the diameter of (0, ±1)-vectors. Ars Mathematica Contemporanea, Tome 13 (2017) no. 1, pp. 1-13. doi : 10.26493/1855-3974.935.4e0. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.935.4e0/

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