Author(s): Jin Qian
Series: PhD thesis at Ohio State University
Year: 2000
A b s tra c t ....................................................................................................................... ii
A cknow ledgm ents ...................................................................................................... iii
V i t a ................................................................................................................................. iv
C H A PTER .............................................................................................................. PAGE
1 Introduction to Com binatorial In e q u a litie s ........................................... 1
1.1 The History of Combinatorial Inequalities ............................................... 1
1.2 Outline of the dissertation ........................................................................... 13
2 Quasi-Polynom ial S em i-L attice .................................................................... 14
2.1 Introduction to Quasi-Polynomial S em i-L attice .......................... 14
2.2 Statem ents and Proofs of Some Classic T h e o re m s ................... 22
2.3 Proof of the T h e o re m s ........................................................................... 23
3 The extrem e case of the Frankl-Ray-Chaudhuri-W ilson Theorem 30
3.1 A New Proof of the Ray-Chaudhuri-Wilson type Inequalities ............. 30
3.2 Characterization of the Extreme Case of the Frankl-Ray-Chaudhuri-
Wilson Inequality ............................................................................................. 35
4 M odular C om binatorial In eq u alities ........................................................... 53
4.1 Some Basic Modular Combinatorial Inequalities ..................................... 53
4.2 On the Mod-p Alon-Babai-Suzuki Inequality .......................................... 57
5 M iscellaneous R e s u lts ....................................................................................... 69
5.1 Special Cases of Snevily;s Conjecture ........................................................ 69
5.2 The Extreme Case of the Alon-Babai-Suzuki Type Inequality ............ 78
B ib lio g rap h y .................................................................................................................... 93
