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Large Sets of Nearly Orthogonal Vectors

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Abstract.

It is shown that there is an absolute positive constant δ>0, so that for all positive integers k and d , there are sets of at least dδlog2(k+2)/log2log2(k+2) nonzero vectors in R d, in which any k+1 members contain an orthogonal pair. This settles a problem of Füredi and Stanley.

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Authors and Affiliations

  1.  Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel. email: noga@math.tau.ac.il, , , , , , IL

    Noga Alon

  2.  AT & T Bell Labs, Murray Hill, NJ 07974, USA. email: ms@research.att.com, , , , , , US

    Mario Szegedy

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  1. Noga Alon
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  2. Mario Szegedy
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Received: August 9, 1995 Revised: November 10, 1997

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Alon, N., Szegedy, M. Large Sets of Nearly Orthogonal Vectors. Graphs Comb 15, 1–4 (1999). https://doi.org/10.1007/PL00021187

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  • DOI: https://doi.org/10.1007/PL00021187

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