Erd\H{o}s Rado Sunflower Theorem for Shifted Families

Mathematics > Combinatorics [Submitted on 1 Jun 2026 (v1), last revised 8 Jun 2026 (this version, v2)] Title:Erdős Rado Sunflower Theorem for Shifted Families View PDF HTML (experimental)Abstract:Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erdős-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \leq C^k$. In this paper, we prove the conjecture for shifted families. Submission history From: Tapas Kumar Mishra [view email][v1] Mon, 1 Jun 2026 11:00:52 UTC (12 KB) [v2] Mon, 8 Jun 2026 11:42:11 UTC (11 KB) Current browse context: math.CO References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.