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December 2007 Flag algebras
Alexander A. Razborov
J. Symbolic Logic 72(4): 1239-1282 (December 2007). DOI: 10.2178/jsl/1203350785

Abstract

Asymptotic extremal combinatorics deals with questions that in the language of model theory can be re-stated as follows. For finite models $M, N$ of an universal theory without constants and function symbols (like graphs, digraphs or hypergraphs), let $p(M,N)$ be the probability that a randomly chosen sub-model of $N$ with $|M|$ elements is isomorphic to $M$. Which asymptotic relations exist between the quantities $p(M₁,N),…, p(M_h,N)$, where $M_1,…,M_h$ are fixed “template” models and $|N|$ grows to infinity? In this paper we develop a formal calculus that captures many standard arguments in the area, both previously known and apparently new. We give the first application of this formalism by presenting a new simple proof of a result by Fisher about the minimal possible density of triangles in a graph with given edge density.

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Alexander A. Razborov. "Flag algebras." J. Symbolic Logic 72 (4) 1239 - 1282, December 2007. https://doi.org/10.2178/jsl/1203350785

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1146.03013
MathSciNet: MR2371204
Digital Object Identifier: 10.2178/jsl/1203350785

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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