{"id":"palomar/PALOMAR-2026-09-05-000001","url":"https://github.com/npflueger/brill-noether-graphs/tree/7987ddbab4f757592e2d2b52565f2c3670e4ff6b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-05-000001-v1.json","repo":"https://github.com/npflueger/brill-noether-graphs","tags":["math.CO","msc:05C57","msc:14T15","msc:14H51","brill-noether","chip-firing","lean-formalization"],"score":0,"title":"Brill--Noether generality and gonality for chains of cycles and theta graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Nathan Pflueger"],"reviews":0,"subject":"math.CO","summary":"This repository formalizes Brill--Noether generality for chains whose factors may be cycles or theta graphs, subject to a genericity condition on path lengths and an evenly-marked condition on the theta factors. A graph is called Brill--Noether general if the possible degrees and ranks of its chip configurations, in the sense of Baker and Norine, match the behavior of a general algebraic curve. Here we use only the existential form of Brill--Noether generality, without computing dimensions. Following Cools--Draisma--Payne--Robeva, we also formalize a mild vanishing-order condition that…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-05","reactions":{},"formalized":true,"formalizes":[{"title":"A tropical proof of the Brill--Noether theorem","identifier":"https://doi.org/10.1016/j.aim.2012.02.019","relationship":"formalizes"},{"title":"(Hurwitz-)Brill--Noether general marked graphs via the Demazure product","identifier":"https://arxiv.org/abs/2201.12316","relationship":"formalizes"},{"title":"Twice-marked banana graphs & Brill--Noether generality","identifier":"https://doi.org/10.5802/alco.443","relationship":"formalizes"}]}