{"id":"hexagon/2610.00709","pdf":"https://hexagonmath.org/pdf/2610.00709v1","url":"https://hexagonmath.org/abs/2610.00709v1","tags":["math.CO","cs.DM","msc:60C05","msc:05A16","msc:68R15","Chvátal–Sankoff constants","Collatz–Wielandt certificates","longest common subsequence","transfer matrices"],"score":0,"title":"Upper bounds for the Chvátal–Sankoff constants $\\gamma_k$, $k\\ge3$","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.PR","summary":"Lueker (J. ACM 56(3), 2009) constructed a family of finite-state machines $\\mathcal{M}_h$ whose associated transfer matrices yield upper bounds on the Chvátal–Sankoff constants $\\gamma_k$, and proved (his Theorem 3.26) that these bounds converge to $\\gamma_k$ for every alphabet size $k$. He published values only for $k=2$. For $k\\ge3$ the best upper bounds we were able to find in the literature in September 2026 were still those of Dančík's 1994 thesis: subsequent work generalising Lueker has generalised his Section 2, the lower bound. We implement $\\mathcal{M}_h$ for arbitrary $k$. One…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}