The counting lemma for regular k-uniform hypergraphs
By B. Nagle, Vojtech Rödl, Mathias Schacht. 2006
97 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/f45a7d7fd2a7a1b080c2b98831cd3357950ee54c
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- David Conlon
- Terence Tao
- William T. Gowers
- Wojciech Samotij
- Mathias Schacht
- Nikos Frantzikinakis
- Ben Joseph Green
- Charles Bordenave
Citations in the corpus
- An inverse theorem for the Gowers U^3 norm (2005, methodology): “ntially closer in spirit to Roth’s original argument than the other proofs. Even more recently there have been a number of other proofs of this theorem by other methods, such as hypergraph regularity [27, 45, 46, 50, 51, 52] or “discrete ergodic theory” [59]. This theorem and its various proofs have”
- On the KŁR conjecture in random graphs (2013, methodology): “ that a.a.s any regular partition of a subgraph of the random hypergraph has a corresponding counting lemma. The main obstacle here is to prove a sparse counterpart to the hypergraph regularity lemma [37, 38, 65, 74, 84]. This should be a comparatively straightforward hybrid of the hypergraph regula”
- Combinatorial theorems in sparse random sets (2010, background): “´edi) = ˆ 0, if p<cn−1/(k−1), 1, if p>Cn−1/(k−1). One approach to proving Szemer´edi’s theorem is known as the hypergraph removal lemma. Proved independently by Nagle, Ro¨dl, Schacht and Skokan [40, 51] and by the second author [21] (see also [61]), this theorem states that for every δ>0 an”
- Norm convergence of multiple ergodic averages for commuting transformations (2007, background): “This theorem is faintly reminiscent of the “hypergraph counting lemmas” which appear for instance in [17], [11], [23].”
- What is good mathematics (2007, background): “other in the correct order. Indeed the final versions of the regularity lemma, and the companion “counting lemmas” from which one could deduce Szemer´edi’s theorem, have only appeared rather recently ([22], [24], [25], [26], [14], ...). It is also worth mentioning a very instructive counterexample [1”