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A273096
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Number of rotationally inequivalent minimal relations of roots of unity of weight n.
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1
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1, 0, 1, 1, 0, 1, 1, 3, 3, 4, 6, 18, 69
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OFFSET
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0,8
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COMMENTS
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In this context, a relation of weight n is a multiset of n roots of unity which sum to zero, and it is minimal if no proper nonempty sub-multiset sums to zero. Relations are rotationally equivalent if they are obtained by multiplying each element by a common root of unity.
Mann classified the minimal relations up to weight 7, Conway and Jones up to weight 9, and Poonen and Rubinstein up to weight 12.
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LINKS
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EXAMPLE
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Writing e(x) = exp(2*Pi*i*x), then e(1/6)+e(1/5)+e(2/5)+e(3/5)+e(4/5)+e(5/6) = 0 and this is the unique (up to rotation) minimal relation of weight 6.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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