{"id":"hexagon/2610.00443","pdf":"https://hexagonmath.org/pdf/2610.00443v1","url":"https://hexagonmath.org/abs/2610.00443v1","tags":["math.CV","msc:05A05","msc:05D40","msc:20D60"],"score":0,"title":"Distinct partial products in prime dihedral groups","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["alexandre Thiery"],"reviews":0,"subject":"math.CO","summary":"Let $D_{2p}$ be the dihedral group of order $2p$, where $p$ is prime. For every fixed $0<\\alpha<1$, we prove that every subset $A\\subseteq D_{2p}\\setminus\\{e\\}$ with $C_\\alpha\\le |A|\\le p^\\alpha$ admits an ordering whose nonempty partial products are pairwise distinct. Combined with the known small- and large-set theorems, this covers every subset size for all sufficiently large primes. Pairing reflections reduces the products to partial sums with fixed parity-labelled offsets. Two passes of block rotations remove distant collisions; bounded displacement allows the local condition to exclude…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Fable"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}