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Lattices and quadratic forms from tight frames in Euclidean spaces. (arXiv:1704.07735v1 [math.NT])
来源于:arXiv
We continue our investigation of integral spans of tight frames in Euclidean
spaces. In a previous paper, we considered the case of an equiangular tight
frame (ETF), proving that if its integral span is a lattice then the frame must
be rational, but overlooking a simple argument in the reverse direction. Thus
our first result here is that the integral span of an ETF is a lattice if and
only if the frame is rational. Further, we discuss conditions under which such
lattices are eutactic and perfect and, consequently, are local maxima of the
packing density function in the dimension of their span. In particular, the
unit (276, 23) equiangular tight frame is shown to be eutactic and perfect.
More general tight frames and their norm-forms are considered as well, and
definitive results are obtained in dimensions two and three. 查看全文>>