Random and deterministic versions of extremal poset problems
نویسنده
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER
منابع مشابه
Random conformal snowflakes
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the multifractal analysis of harmonic measure. We argue that, searching for extremals in such problems, one should work with random fractals rather than deterministic one...
متن کاملUniversal Poisson and Normal Limit Theorems in Graph Coloring Problems with Connections to Extremal Combinatorics
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior of the ratio of the number of edges in the graph and the number of colors, and works for any graph sequence deterministic or random. The proofs are based on moment calculations which relates to res...
متن کاملStability results for random discrete structures
Two years ago, Conlon and Gowers, and Schacht proved general theorems that allow one to transfer a large class of extremal combinatorial results from the deterministic to the probabilistic setting. Even though the two papers solve the same set of long-standing open problems in probabilistic combinatorics, the methods used in them vary significantly and therefore yield results that are not compa...
متن کاملExtremal Problems on Finite Sets and Posets
The overarching theme of the thesis is the investigation of extremal problems involving forbidden partially ordered sets (posets). In particular, we will be concerned with the function La(n, P ), defined to be the maximum number of sets we can take in the Boolean lattice 2[n] without introducing the relations of a poset P as containment relations among the sets. This function plays an analogous...
متن کاملQuasi-Random Hypergraphs and Extremal Problems for Hypergraphs
The regularity lemma was originally developed by Szemerédi in the seventies as a tool to resolve a long standing conjecture of Erdős and Turán, that any subset of the integers of positive upper density contains arbitrary long arithmetic progressions. Soon this lemma was recognized as an important tool in extremal graph theory and it also has had applications to additive number theory, discrete ...
متن کامل