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Some six-dimensional rigid forms
<span title="2005-01-04">2005</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2004-02-15">2004</span>
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<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0401191v2">arXiv:math/0401191v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i5qqs46vingcplzjwhgb75a3va">fatcat:i5qqs46vingcplzjwhgb75a3va</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0401191v2">arXiv:math/0401191v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i5qqs46vingcplzjwhgb75a3va">fatcat:i5qqs46vingcplzjwhgb75a3va</a> </span>
<span title="2004-01-16">2004</span>
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<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0401191v1">arXiv:math/0401191v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mbiipwtrrrf3zpl3g2aldytldi">fatcat:mbiipwtrrrf3zpl3g2aldytldi</a> </span>
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One can always decompose Dirichlet-Voronoi polytopes of lattices non-trivially into a Minkowski sum of Dirichlet-Voronoi polytopes of rigid lattices. In this report we show how one can enumerate all rigid positive semidefinite quadratic forms (and thereby rigid lattices) of a given dimension d. By this method we found all rigid positive semidefinite quadratic forms for d = 5 confirming the list of 7 rigid lattices by Baranovskii and Grishukhin. Furthermore, we found out that for d <= 5 the
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... ency graph of primitive L-type domains is an infinite tree on which GL_d(Z) acts. On the other hand, we demonstrate that in d = 6 we face a combinatorial explosion.
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