An improved lower bound for the maximal length of a multivector
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A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for n-vectors, with \(n>2\), since the few exactly known values seem to grow only linearly with vector space dimension, whereas the new lower bound grows at power \(n-1\) like the best known upper bound. This result has implications in quantum chemistry for the compression of information contained in an electronic wave function.
KeywordsElectronic wave functions Antisymmetric tensor compression Multi-vector length Grassmann space Exterior algebra
B. Mourrain and A. Galligo, are ackowledged for discussions that have helped the author in putting his arguments in the present form. In particular, B. Mourrain has provided precise algebraic geometry hints and references.
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