{"id":"palomar/PALOMAR-2026-10-09-000009","url":"https://github.com/npflueger/brill-noether-graphs/tree/bfa274b00e6e559f34f3307d33c4aae52825778e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-09-000009-v1.json","repo":"https://github.com/npflueger/brill-noether-graphs","tags":["math.CO","math.AG","msc:05C57","msc:14T15","msc:14H51","graph-theory","brill-noether","algebraic-geometry","chip-firing"],"score":0,"title":"Brill--Noether existence and rank for graphs through genus six","trust":"high","domain":"math.CO","source":"palomar","authors":["Nathan Pflueger"],"reviews":0,"subject":"math.CO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-09","reactions":{},"formalized":true}