Corpus ID: 3590498

An Arithmetic Analogue of Fox's Triangle Removal Argument

@article{Hatami2013AnAA,
  title={An Arithmetic Analogue of Fox's Triangle Removal Argument},
  author={P. Hatami and Sushant Sachdeva and Madhur Tulsiani},
  journal={ArXiv},
  year={2013},
  volume={abs/1304.4921}
}
  • P. Hatami, Sushant Sachdeva, Madhur Tulsiani
  • Published 2013
  • Mathematics, Computer Science
  • ArXiv
  • We give an arithmetic version of the recent proof of the triangle removal lemma by Fox [Fox11], for the group F n . A triangle in F n is a tuple (x,y,z) such that x + y + z = 0. The triangle removal lemma for F n states that for every " > 0 there is a � > 0, such that if a subset A of F n requires the removal of at least " · 2 n elements to make it triangle-free, then it must contain at least � · 2 2n triangles. We give a direct proof which gives an improved lower bound for � (as a function of… CONTINUE READING
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    References

    SHOWING 1-10 OF 24 REFERENCES
    A combinatorial proof of the Removal Lemma for Groups
    • 64
    • PDF
    A new proof of the graph removal lemma
    • J. Fox
    • Mathematics, Computer Science
    • ArXiv
    • 2010
    • 133
    • Highly Influential
    • PDF
    Lower bounds for testing triangle-freeness in Boolean functions
    • 24
    • PDF
    Testing Odd-Cycle-Freeness in Boolean Functions
    • 10
    • PDF
    A new proof of Szemerédi's theorem
    • 720
    • PDF
    A Unified Framework for Testing Linear-Invariant Properties
    • 40
    • PDF
    Graph removal lemmas
    • 73
    • Highly Influential
    • PDF