نتایج جستجو برای: sunflowers
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A Sunflower is a subset S of a lattice, with the property that the meet of any two elements in S coincides with the meet of all of S. The Sunflower Lemma of Erdös and Rado [2] asserts that a set of size at least 1 + k!(t − 1)k of elements of rank k in a Boolean Lattice contains a sunflower of size t. We develop counterparts of the Sunflower Lemma for distributive lattices, graphic matroids, and...
Hybridization is frequent in many organismal groups, but its role in adaptation is poorly understood. In sunflowers, species found in the most extreme habitats are ancient hybrids, and new gene combinations generated by hybridization are speculated to have contributed to ecological divergence. This possibility was tested through phenotypic and genomic comparisons of ancient and synthetic hybrid...
A sunflower with p petals consists of sets whose pairwise intersections are identical. The goal the problem is to find smallest r=r(p,k) such that any family rk distinct k-element contains a petals. Building upon breakthrough Alweiss, Lovett, Wu and Zhang from 2019, Rao proved r=O(plog(pk)) suffices; this bound was reproved by Tao in 2020. In short note we record r=O(plogk) suffices, using mino...
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