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Extensions of Classic Theorems in Ex...

Das, Shagnik.

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Extensions of Classic Theorems in Extremal Combinatorics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Extensions of Classic Theorems in Extremal Combinatorics./
Author:	Das, Shagnik.
Description:	152 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-09(E), Section: B.
Contained By:	Dissertation Abstracts International75-09B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3622434
ISBN:	9781303941757

Extensions of Classic Theorems in Extremal Combinatorics.
Das, Shagnik.

Extensions of Classic Theorems in Extremal Combinatorics. - 152 p.

Source: Dissertation Abstracts International, Volume: 75-09(E), Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2014.

This item must not be sold to any third party vendors.

Extremal combinatorics deals with the following fundamental question: how large can a structure be without containing forbidden configurations? The structures studied are extremely flexible, allowing for a wide range of applications to diverse fields such as theoretical computer science, operations research, discrete geometry and number theory. Moreover, tools from probability theory, algebra and analysis have proven incredibly useful, spurring the development of new techniques in combinatorics. This synergy between different fields has led to incredible growth in recent decades, inspiring numerous directions for research.

ISBN: 9781303941757Subjects--Topical Terms:

515831
Mathematics.

Extensions of Classic Theorems in Extremal Combinatorics.
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020 $a 9781303941757
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100 1 $a Das, Shagnik. $3 3173529
245 1 0 $a Extensions of Classic Theorems in Extremal Combinatorics.
300 $a 152 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-09(E), Section: B.
500 $a Adviser: Benjamin Sudakov.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2014.
506 $a This item must not be sold to any third party vendors.
520 $a Extremal combinatorics deals with the following fundamental question: how large can a structure be without containing forbidden configurations? The structures studied are extremely flexible, allowing for a wide range of applications to diverse fields such as theoretical computer science, operations research, discrete geometry and number theory. Moreover, tools from probability theory, algebra and analysis have proven incredibly useful, spurring the development of new techniques in combinatorics. This synergy between different fields has led to incredible growth in recent decades, inspiring numerous directions for research.
520 $a In this dissertation, we present new extensions of classic theorems in extremal combinatorics, employing probabilistic and analytic arguments to solve problems connected to number theory and coding theory. In Chapter 2, we greatly improve the bounds for the rainbow Turan problem for even cycles, a problem merging the graph theoretic disciplines of Turan theory and graph colouring. In Chapter 3, we use the analytic method of flag algebras to study a variant of Turan's theorem proposed by Erdo&huml;s. We then shift to extremal set theory, and in Chapter 4 study the supersaturation problem for the Erdo&huml;s-Ko-Rado Theorem. In Chapter 5 we discuss a probabilistic measure of supersaturation for intersecting families, introduced recently by Katona, Katona and Katona. These problems represent the various fields within extremal combinatorics that the author has worked in.
590 $a School code: 0031.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
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690 $a 0642
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertation Abstracts International $g 75-09B(E).
790 $a 0031
791 $a Ph.D.
792 $a 2014
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3622434