We investigate, using purely combinatorial methods, structural and algorithmic properties of linear equivalence classes of divisors on tropical curves. In particular, an elementary proof of the RiemannRoch theorem for tropical curves, similar to the recent proof of the Riemann-Roch theorem for graphs by Baker and Norine, is presented. In addition, a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to the rank of D on the corresponding metric graph is confirmed, and an algorithm for computing the rank of a divisor on a tropical curve is constructed.
The central quantity in the Riemann-Roch theorem is the rank of a divisor and the efficient computation of rank is a natural problem, attributed to Hendrik Lenstra (see REF ).
Rank of divisors on tropical curves
J. Combin. Theory Ser. A 120, no. 7, 1521-1538 (2013)
Mathematics Computer Science