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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Frankl-Rödl-type theorems for codes and permutations
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by Peter Keevash and Eoin Long PDF
Trans. Amer. Math. Soc. 369 (2017), 1147-1162 Request permission

Abstract:

We give a new proof of the Frankl-Rödl theorem on forbidden intersections, via the probabilistic method of dependent random choice. Our method extends to codes with forbidden distances, where over large alphabets our bound is significantly better than that obtained by Frankl and Rödl. We also apply our bound to a question of Ellis on sets of permutations with forbidden distances and to establish a weak form of a conjecture of Alon, Shpilka and Umans on sunflowers.
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Additional Information
  • Peter Keevash
  • Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
  • MR Author ID: 670477
  • Email: Peter.Keevash@maths.ox.ac.uk
  • Eoin Long
  • Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
  • Address at time of publication: School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
  • MR Author ID: 1040049
  • Email: Eoin.Long@maths.ox.ac.uk, eoinlong@post.tau.ac.il
  • Received by editor(s): February 25, 2014
  • Received by editor(s) in revised form: February 12, 2015
  • Published electronically: October 7, 2016
  • Additional Notes: This research was supported in part by ERC grant 239696 and EPSRC grant EP/G056730/1.
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1147-1162
  • MSC (2010): Primary 05D05; Secondary 05D40, 94B65
  • DOI: https://doi.org/10.1090/tran/7015
  • MathSciNet review: 3572268