Work

Sunflowers and Quasi-Sunflowers from Randomness Extractors

Year: 2018

Type: article

Abstract: The Erdös-Rado sunflower theorem (Journal of Lond. Math. Soc. 1960) is a fundamental result in combinatorics, and the corresponding sunflower conjecture is a central open problem. Motivated by applications in complexity theory, Rossman (FOCS 2010) extended the result to quasi-sunflowers, where similar conjectures emerge about the optimal parameters for which it holds. In this work, we exhibit a surprising connection between the existence of sunflowers and quasi-sunflowers in large enough set systems, and the problem of constructing (or existing) certain randomness extractors. This allows us to re-derive the known results in a systematic manner, and to reduce the relevant conjectures to the problem of obtaining improved constructions of the randomness extractors.

Source: DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)

DOI: 10.4230/lipics.approx-random.2018.51

Authors: Li, Xin, Lovett, Shachar, Zhang, Jiapeng

Institutions: Johns Hopkins University, University of California San Diego

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: AF: Small: Randomness in Computation - Old Problems and New Directions, AF: Small: Rare Events - New Probabilistic and Algorithmic Techniques