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Hyperdeterminants on semilattices

Abstract : We compute hyperdeterminants of hypermatrices whose indices belongs in a meet-semilattice and whose entries depend only of the greatest lower bound of the indices. One shows that an elementary expansion of such a polynomial allows to generalize a theorem of Lindström to higher-dimensional determinants. And we gave as an application generalizations of some results due to Lehmer, Li and Haukkanen.
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https://hal.archives-ouvertes.fr/hal-00085204
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Submitted on : Wednesday, November 22, 2006 - 9:01:16 AM
Last modification on : Tuesday, October 19, 2021 - 5:34:00 PM
Long-term archiving on: : Thursday, September 23, 2010 - 4:33:17 PM

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Jean-Gabriel Luque. Hyperdeterminants on semilattices. Linear and Multilinear Algebra, Taylor & Francis, 2007, 56 (3), pp.333-344. ⟨hal-00085204v3⟩

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