A tropical linear series is combinatorial limit if and only if it is structured, and every strongly recursive tropical linear series is combinatorial limit; the reverse inclusion fails from rank three onward.
Combinatorial flag arrangements
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abstract
We introduce combinatorial objects named matricubes that provide a generalization of the theory of matroids. As matroids provide a combinatorial axiomatization of hyperplane arrangements, matricubes provide a combinatorial axiomatization of arrangements of initial flags in a vector space. We give cryptomorphic axiomatic systems in terms of rank function, flats, circuits, and independent sets, and formulate a duality concept. We also provide precise links between matricubes, permutation arrays and matroids, and raise several open questions.
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Relating Different Definitions of Linear Series on Tropical Curves
A tropical linear series is combinatorial limit if and only if it is structured, and every strongly recursive tropical linear series is combinatorial limit; the reverse inclusion fails from rank three onward.