- Abstract:
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Frankl and Füredi conjectured in 1989 that the maximum Lagrangian of all r-uniform hypergraphs of fixed size m is realised by the initial segment of the colexicographic order. In particular, in the principal case m=(tr) that every H⊆N(r)of size (tr) satisfies max{∑A∈H∏i∈Ayi:y1,y2,…≥0;∑i∈Nyi=1}≤[Formula presented](tr). We prove the above statement for all r≥4 and large values of t (the case r = 3 was settled by Talbot in 2002). More generally, we show for any r≥4 that the Frankl-Füredi conjec...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted Manuscript
- Files:
-
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(pdf, 259.5kb)
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- Publisher copy:
- 10.1016/j.endm.2017.07.072
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- Publisher:
- Elsevier Publisher's website
- Journal:
- Electronic Notes in Discrete Mathematics Journal website
- Volume:
- 61
- Pages:
- 1055-1059
- Publication date:
- 2017-08-03
- DOI:
- ISSN:
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1571-0653
- Pubs id:
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pubs:938279
- URN:
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uri:3e8094d6-8624-4e38-8bfa-4e0f1db5c18a
- UUID:
-
uuid:3e8094d6-8624-4e38-8bfa-4e0f1db5c18a
- Local pid:
- pubs:938279
- Copyright holder:
- Elsevier B.V.
- Copyright date:
- 2017
- Notes:
- Copyright © 2017 Elsevier B.V.This is the accepted manuscript version of the article. The final version is available online from Elsevier at: https://doi.org/10.1016/j.endm.2017.07.072
Journal article
Lagrangians of hypergraphs: The Frankl-Füredi conjecture holds almost everywhere
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