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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 26, Issue 6 (Nov 2014)


Dressians, tropical Grassmannians, and their rays

Sven Herrmann
  • School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK
  • Email:
/ Michael Joswig
  • Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany
  • Email:
/ David E Speyer
  • Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, USA
  • Email:
Published Online: 2012-07-20 | DOI: https://doi.org/10.1515/forum-2012-0030


The Dressian Dr(k,n) parametrizes all tropical linear spaces, and it carries a natural fan structure as a subfan of the secondary fan of the hypersimplex Δ(k,n). We explore the combinatorics of the rays of Dr(k,n), that is, the most degenerate tropical planes, for arbitrary k and n. This is related to a new rigidity concept for configurations of n - k points in the tropical k - 1-torus. Additional conditions are given for k = 3. On the way, we compute the entire fan Dr(3,8).

Keywords: Matroid polytopes; Grassmann–Plücker relations

MSC: 52B40; 14P99

About the article

Received: 2012-03-18

Revised: 2012-05-29

Published Online: 2012-07-20

Published in Print: 2014-11-01

Funding Source: German Academic Exchange Service (DAAD)

Award identifier / Grant number: Postdoc-Program

Funding Source: DFG

Award identifier / Grant number: Priority Program 1489 Experimental Methods in Algebra, Geometry and Number Theory

Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0030. Export Citation

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