Results 1 to 10 of about 171 (78)
UPPER BOUNDS FOR SUNFLOWER-FREE SETS
Forum of Mathematics, Sigma, 2017 A collection of $k$ sets is said to form a $k$ -sunflower ...
ERIC NASLUND, WILL SAWIN
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On cap sets and the group-theoretic approach to matrix multiplication
Discrete Analysis, 2017 On cap sets and the group-theoretic approach to matrix multiplication, Discrete Analysis 2017:3, 27pp. A famous problem in computational complexity is to obtain a good estimate for the number of operations needed to compute the product of two $n\times n$
Jonah Blasiak +6 more
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The Sunflower Conjecture Proven
, 2022 8 pages to fix the error of Ver. 2. Please visit https://sites.psu.edu/sunflowerconjecture/2022/12/18/index-page/ for additional information on the ...
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A Proof of the Sunflower Conjecture
We prove the Sunflower Conjecture of Erdős and Rado (1960): there exists a constant C(k) depending only on k such that any family of more than C(k)^r sets of size r contains a k-sunflower. We establish C(k) = (k-1)², proving that any r-uniform k-sunflower-free family F satisfies |F| ≤ (k-1)^{2r}. For k = 3, this gives |F| ≤ 4^r.
Mitchell, Cody, Claude, Opus
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On the Sunflower Conjecture: Computational Bounds and an Unsuccessful Proof Attempt
CORRECTION NOTICE (v2, January 15, 2026): Version 1 claimed a proof of the Sunflower Conjecture. This claim is RETRACTED. Mathematician Thomas Bloom identified a fundamental error: Lemma 4.2 incorrectly bounds the piercing number independently of r, which is known to be impossible. The main theorem does not follow.
Mitchell, Cody, Claude, Opus
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It is well known that Erdős Matching Conjecture concerns the maximum number of hyperedges in an $r$-uniform hypergraph with bounded matching number. As a generalization, it is natural to ask for the maximum number of copies of subhypergraphs. Given integers $r\geq2$ and $k\ge 1$, let $S_{r-1,k}^r$ denote the $r$-uniform hypergraph with hyperedges ...
Zhou, Junpeng, Yuan, Xiying
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Exact Values and a Conjectured Formula for Maximum Sunflower-Free Families
Version 3 — First Public Release (January 14, 2026) Major revision with new theoretical framework and extended computations. What's New in V3: • NEW: Conjectured formula m(n,3) = (8/3)·(3/2)^(n-1) — exact for n=2,3,4, matches to 98.8% for n=5,6,7,8 • NEW: Optimized parallel solver with intersection indexing (P1-P4 improvements) • NEW:
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Novel roles of HSFs and HSPs, other than relating to heat stress, in temperature-mediated flowering. [PDF]
Ann Bot, 2023 Majee A, Kumari D, Sane VA, Singh RK.
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Monotone Circuit Lower Bounds from Robust Sunflowers. [PDF]
Algorithmica, 2022 Cavalar BP, Kumar M, Rossman B.
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Recent Evidence on Polycyclic Aromatic Hydrocarbon Exposure. [PDF]
Healthcare (Basel), 2023 Zhao X, Gao J, Zhai L, Yu X, Xiao Y.
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