Publications de l'Institut Mathématique (Beograd)
Vol. 72(86), pp. 23-28 (2002)
VERIFICATION OF ATIYAH'S CONJECTURE FOR SOME NONPLANAR CONFIGURATIONS WITH DIHEDRAL SYMMETRY
Dragomir \v Z. \DJ okovi\'cDepartment of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Abstract: To an ordered $N$-tuple of distinct points in the three-dimensional Euclidean space, Atiyah has associated an ordered $N$-tuple of complex homogeneous polynomials in two variables of degree $N-1$, each determined only up to a scalar factor. He has conjectured that these polynomials are linearly independent. In this note, it is shown that Atiyah's conjecture is true if $m$ of the points are on a line $L$ and the remaining $n=N-m$ points are the vertices of a regular $n$-gon whose plane is perpendicular to $L$ and whose centroid lies on $L$.
Keywords: Atiyah conjecture
Classification (MSC2000): 51M04; 51M16; 70G25
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Electronic version published on: 23 Nov 2003. This page was last modified: 24 Nov 2003.
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