Kapranov rank vs. tropical rank

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dc.creatorKim, K. H.
dc.creatorRoush, F. W.
dc.date2005-03-02
dc.date2005-03-16
dc.date.accessioned2026-07-07T05:17:37Z
dc.date.available2026-07-07T05:17:37Z
dc.descriptionWe show that determining Kapranov rank of tropical matrices is not only NP-hard over any infinite field but also if solving Diophantine equations over the rational numbers is undecidable, then determining Kapranov rank over the rational numbers is undecidable. We prove that Kapranov rank of tropical matrices is not bounded in terms of tropical rank, answering a question of Develin, Santos, and Sturmfels.
dc.descriptionReplacement is to fill a gap in the proof of Theorem 3.1
dc.identifierhttps://arxiv.org/abs/math/0503044
dc.identifierhttp://arxiv.org/abs/math/0503044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74369
dc.subjectCombinatorics
dc.subject15A99
dc.titleKapranov rank vs. tropical rank
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