Tropical Linear Spaces

  • Authors:

  • David E. Speyer

  • Affiliations:

  • speyer@math.mit.edu

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2008

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Abstract

We define the tropical analogues of the notions of linear spaces and Plücker coordinates and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated dualization and transverse intersection to be constructible. Our main result is that all constructible tropical linear spaces have the same $f$-vector and are “series-parallel”. We conjecture that this $f$-vector is maximal for all tropical linear spaces, with equality precisely for the series-parallel tropical linear spaces. We present many partial results towards this conjecture.