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Search: id:A089676
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| A089676 |
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Maximum size of a set of points S in {0,1}^d such that every angle determined by three points in S is acute. |
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+0
1
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OFFSET
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0,2
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COMMENT
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If k<=m<=n, a(k+2m)>=a(k)a(m), a(k+2m+3n)>=a(k)a(m)a(n). a(n) >= 2*floor[(sqrt(6)/9)(2/sqrt(3))^n], approx 0.544*1.155^n.
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REFERENCES
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L. Danzer and B. Gruenbaum, Uber zwei Probleme bezuglich konvexer Korper von P. Erdos und von K. L. Klee, Math. Zeitschrift 79 (1962) 95-99.
P. Erdos and Z. Furedi, The greatest angle among n points in the d-dimensional Euclidean space, Annals of Discrete Math. 17 (1983) 275-283.
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LINKS
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D. Bevan, Sets of Points Determining Only Acute Angles and Some Related Colouring Problems, Electronic J. of Combinatorics, 13(1), 2006, #R12.
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EXAMPLE
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a(3)=4: {000, 011, 101, 110}
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CROSSREFS
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Sequence in context: A024683 A071528 A056902 this_sequence A062436 A121269 A056219
Adjacent sequences: A089673 A089674 A089675 this_sequence A089677 A089678 A089679
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KEYWORD
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nonn
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AUTHOR
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David Bevan (dbevan(AT)emtex.com), Jan 06 2004
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