Abstract
What is the most number of vectors inR d such that anyk+1 contain an orthogonal pair? The 24 positive roots of the root systemF 4 inR 4 show that this number could exceeddk.
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Frankl, P.: Orthogonal vectors in then-dimensional cube and codes with missing distances,Combinatorica 6, 279–285 (1986)
Frankl, P., Rödl, V.: Forbidden intersections,Trans. Amer. Math. Soc. 300, 259–286 (1987)
Graham, R.L., Rothschild, B.L., Spencer, J.:Ramsey Theory, Wiley Interscience, 1980. (2nd edition 1990)
Larman, D.G., Rogers, C.A.: The realization of distances whithin sets in eucledian space,Mathematika 19, 1–24 (1972)
Moshe Rosenfeld, Almost orthogonal lines, inE d, DIMACS Series in Discrete Math.4, 489–492 (1991)
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The research was done while the author Z. Füredi visited the Department of Mathematics at Massachusetts Institute of Technology. Research supported in part by the Hungarian National Science Foundation under grant No. 1812. Research supported in part by NSF grants.
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Füredi, Z., Stanley, R. Sets of vectors with many orthogonal paris:. Graphs and Combinatorics 8, 391–394 (1992). https://doi.org/10.1007/BF02351595
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DOI: https://doi.org/10.1007/BF02351595