Brill--Noether existence and rank for graphs through genus six
This repository proves Baker's Brill--Noether existence conjecture for finite graphs of genus at most six. The conjecture states that if G is a finite connected loopless multigraph, with genus defined to be g = E-V+1, then for all nonnegative integers d, r, there exists a configuration of d chips on G with Baker--Norine rank at least r provided that the Brill--Noether number rho = g - (r+1)(g-d+r) is nonnegative. To the author's knowledge, this is a new result, extending a result of Atanasov and Ranganathan from genus five to six. Two generalizations are also included. First, in genus at…
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