Dressians, Tropical Grassmannians, and Their Rays

Details Dressians, Tropical Grassmannians, and Their Rays Dressians, Tropical Grassmannians, and Their Rays

2011-12-06

arxiv.org/abs/1112.1278v2

Mathematics

Combinatorics

Major revision: new Theorem 7 proofs former Conjecture 25; additional co-author. 18 pages, 6 figures

Scientific paper

The Dressian Dr(k,n) parametrizes all tropical linear spaces, and it carries a natural fan structure as a subfan of the secondaryfan of the hypersimplex \Delta(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 con?figurations 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).

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