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Lagrangians of hypergraphs II: When colex is best

Gruslys, V; Letzter, S; Morrison, N; (2021) Lagrangians of hypergraphs II: When colex is best. Israel Journal of Mathematics , 242 (2) pp. 637-662. 10.1007/s11856-021-2132-2. Green open access

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Abstract

A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of the colexicographic order has the largest Lagrangian of any r-uniform hypergraph with m hyperedges. We show that this is true when r = 3. We also give a new proof of a related conjecture of Nikiforov for large t and a counterexample to an old conjecture of Ahlswede and Katona.

Type: Article
Title: Lagrangians of hypergraphs II: When colex is best
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11856-021-2132-2
Publisher version: https://doi.org/10.1007/s11856-021-2132-2
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10143608
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