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).
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
We are indebted to an anonymous referee for several very helpful suggestions.
© 2015 by De Gruyter