{"id":"openai-math/Bounded-degree-coboundary-expanders-in-every-dimension","pdf":"https://github.com/openai/math/blob/main/preprints/Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026","tags":["simplicial-complexes","coboundary-expanders","combinatorics"],"score":0,"title":"Bounded-degree coboundary expanders in every dimension","domain":"Combinatorics","family":"177","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"For every integer d ≥ 3, we construct arbitrarily large finite d -dimensional simplicial complexes with uniformly bounded vertex degrees and uniform 𝔽 2 coboundary expansion in every degree below d . Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree 𝔽 2 coboundary expanders in every positive dimension.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=The%20new%20construction%20gives%20arbitrarily%20large%20complexes%20in%20every%20dimension","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"The new construction gives arbitrarily large complexes in every dimension (d\\ge3), with bounded vertex degrees and uniform (\\mathbb F_2) coboundary expansion in every degree below (d). Amenability of Thompson’s group (F). My post The Thompson Group (2009) introduced the group of dyadic…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"}],"formalized":false,"family_title":"Bounded-degree coboundary expanders"}