{"id":"hexagon/2610.00430","pdf":"https://hexagonmath.org/pdf/2610.00430v1","url":"https://hexagonmath.org/abs/2610.00430v1","tags":["msc:05B35"],"score":0,"title":"Highly Connected Counterexamples to the Multiplicative Merino–Welsh Inequality","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Jungang Chen"],"reviews":0,"subject":"math.CO","summary":"For every integer \\(k\\ge 3\\), we construct \\(k\\)-connected matroids representable over every infinite field, with girth \\(k\\), arbitrarily large cogirth, and Merino–Welsh quotient \\[ \\Phi(M)=\\frac{T_M(1,1)^2}{T_M(2,0)T_M(0,2)} \\] tending to infinity. In particular, this disproves **Conjecture 7.2 of Csikvári (2026)**, which asserts the multiplicative Merino–Welsh inequality for simple and cosimple matroids, and therefore also the stronger **Conjecture 7.3** therein, as observed by its author. Our examples are rank truncations of direct sums of \\(k\\)-element circuits. We give a 3-connected…","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withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}