Flag algebras

By Alexander A. Razborov. Journal of Symbolic Logic (JSL), 2007

338 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/02ebbab306cf455e1ee1636877ab263c5065a5b9

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Citations in the corpus

INVARIANT MEASURES CONCENTRATED ON COUNTABLE STRUCTURES (2012, result): “Our countable relational setting is akin to that explored more recently in extremal combinatorics by Razborov [Raz07]; for details see [Aus08a, §4.3] and [Aus08b].”
ON possible Turán densities (2012, background): “A related open question is whether every true inequality π(F) ≤ α admits a finite proof in Razborov’s Cauchy-Schwarz calculus [34, 35] (see also [25, Appendix A]).”
The number of cliques in graphs of given order and size (2007, methodology): “Applying tools developed in [10], he achieved remarkable progress and essentially solved the problem for r = 3 .”
A problem of Erdős and Sós on 3-graphs (2013, methodology): “All the following results presented in the remainder of this section can be found in [20].”
On the KŁR conjecture in random graphs (2013, methodology): “Employing diﬀerent methods, Nikiforov [66] reproved the k = 3 case and also solved the case k = 4.”
Quasirandom permutations are characterized by 4-point densities (2012, background): “The theory of flag algebras developed by Razborov [20] can be applied to permutation limits: a permutation π : A → A is viewed as two binary relations, each giving a linear order on A.”
On exchangeable random variables and the statistics of large graphs and hypergraphs (2008, methodology): “To date, there are some early indications that this parallelism may occasionally bear fruit in the study of finitary questions, such as recent results of Razborov [54, 55] on an instance of the graph-copy problem, although it is surely too early to judge whether a trend may emerge.”
Surveys in Combinatorics 2011: Hypergraph Turán problems (2011, background): “There are several petrol stations along the route, and the total amount of fuel in these stations is sufficient for the route.”
Sidorenko's conjecture for blow-ups (2018, methodology): “We are greatly indebted to Yufei Zhao and also to Leonardo Nagami Coregliano and Sasha Razborov for spotting a substantial error in an earlier version of this paper.”
The clique density theorem (2012, methodology): “The equation thus obtained may then be weakened by a calculation inspired by Razborov’s work ([11], [12]) to the main inequality What is a bit confusing about this estimate is that when we want to use it for learning something about r -cliques, it seems as if we should already know something about…”