TY  - GEN
AU  - Tao, Terence
AU  - Vu, Van H.
TI  - Additive combinatorics
SN  - 9780521170123
U1  - 511.6 
PY  - 2009///
CY  - New Delhi
PB  - Cambridge University Press
KW  - Combinatorial analysis
KW  - Additive combinatorics
KW  - General principles of mathematics
N1  - Includes bibliographical references (p. 488-504) and index
N2  - Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results

ER  -