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.
A tropical proof of the B rill-- N oether theorem
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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.