E d i t o r i a l B o a r d Gerald B . Follan d Bra d G . Osgoo d Robin Forma n (Chair ) Michae l Starbir d 2000 Mathematics Subject Classification. Primar y 05-XX , 11-XX , 28-XX, 30-XX ? 40-XX , 42-XX , 52-XX . Th e illustratio n o n th e fron t cover , "Wh y Alligator s Don' t Hav e censes," wa s create d b y Nanc y K . Brow n an d i s use d wit h permission . The figures o n page s 5 , 11 , 12 , 16 , 19 , 28 , 40 , 48 , 4 9 an d 6 0 ar e court of Yevge n Yampolskiy . For additiona l informatio n an d update s o n thi s book , visi t w w w . a m s . o r g / b o o k p a g e s / s t m l - 3 9 Library o f Congres s Cataloging-in-Publicatio n Dat a Iosevich, Alex , 1967 - A vie w fro m th e to p : analysis , combinatoric s an d numbe r theor y / A Iosevich. p. cm . (Studen t mathematica l library , ISS N 1520-912 1 v. 39 ) Includes bibliographica l references . ISBN 978-0-8218-4397- 0 (alk . paper ) 1. Inequalities (Mathematics ) 2 . Combinatorial analysis . 3 . Number theo I. Title . QA295.I57 200 7 512.9 7—dc22 200706083 Copying an d reprinting . Individua l reader s o f thi s publication , an d nonpr libraries actin g fo r them , ar e permitte d t o mak e fai r us e o f th e material , suc h a copy a chapte r fo r us e i n teachin g o r research . Permissio n i s grante d t o quot e b passages fro m thi s publicatio n i n reviews , provide d th e customar y acknowledgmen the sourc e i s given. Republication, systemati c copying , o r multiple reproductio n o f any materia l i n publication i s permitted onl y unde r licens e fro m th e America n Mathematica l Soci Requests fo r suc h permissio n shoul d b e addresse d t o th e Acquisition s Departme American Mathematica l Society , 20 1 Charles Street , Providence , Rhod e Islan d 029 2294, USA . Request s ca n als o be mad e b y e-mai l t o reprint-permission@ams.org . © 200 7 b y th e America n Mathematica l Society . Al l right s reserved . The America n Mathematica l Societ y retain s al l right s except thos e grante d t o th e Unite d State s Government . Printed i n th e Unite d State s o f America . @ Th e pape r use d i n thi s boo k i s acid-fre e an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability . Visit th e AM S hom e pag e a t http://www.ams.org / 10 9 8 7 6 5 4 3 2 1 1 2 1 1 1 0 0 9 0 8 0 7
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