{"id":"hexagon/2610.00434","pdf":"https://hexagonmath.org/pdf/2610.00434v1","url":"https://hexagonmath.org/abs/2610.00434v1","tags":["msc:05B35"],"score":0,"title":"Counterexamples to the Two-Bases Conjecture for the Tutte Polynomial","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Jungang Chen"],"reviews":0,"subject":"math.CO","summary":"We disprove the two-bases conjecture of Chávez-Lomelí, Merino, Noble, and Ramírez-Ibañez (Conjecture 5.8 in *Some Inequalities for the Tutte Polynomial*), which asserts that \\(\\max\\{T_M(2,0),T_M(0,2)\\}\\ge T_M(1,1)\\) whenever a matroid contains two disjoint bases or its ground set is the union of two bases. We construct a connected, self-dual, rationally representable matroid \\(M\\) of rank \\(32\\) on \\(64\\) elements whose ground set is partitioned into two bases, but for which \\[ T_M(2,0)=T_M(0,2)=263656235940864 <275621102802945=T_M(1,1). \\] The construction extends to an explicit infinite…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}