目錄
Preface
Notations
I Ingredients
1 Number theory
1.1 Divisibility of integers
1.2 Congruences
1.3 The Fundamental Theorem of Number Theory
1.4 Multiplicative number theory
1.5 Additive number theory
2 Combinatorics
2.1 Basic enumeration principles
2.2 Counting lists, sequences, sets, and multisets
2.3 Binomial coefficients and Pascal's Triangle
2.4 Some recurrence relations
2.5 The integer lattice and its layers
3 Group theory
3.1 Finite abelian groups
3.2 Group isomorphisms
3.3 The Fundamental Theorem of Finite Abelian Groups
3.4 Subgroups and cosets
3.5 Subgroups generated by subsets
3.6 Sumsets
II Appetizers
Spherical designs
Caps, centroids, and the game SET
How many elements does it take to span a group?
In pursuit of perfection
The declaration of independence
III Sides
The function vg (n, h)
The function v+(n, h)
The function u(n, m, h)
The function u^(n, m, h)
IV Entrees
A Maximum sumset size
A.1 Unrestricted sumsets
A.1.1 Fixed number of terms
A.1.2 Limited number of terms
A.1.3 Arbitrary number of terms
A.2 Unrestricted signed sumsets
A.2.1 Fixed number of terms
A.2.2 Limited number of terms
A.2.3 Arbitrary numbcr of terms
A.3 Restricted sumsets
A.3.1 Fixed number of terms
A.3.2 Limited number of terms
A.3.3 Arbitrary number of terms
A.4 Restricted signed sumscts
A.4.1 Fixed number of terms
A.4.2 Limited number of terms
A.4.3 Arbitrary number of terms
B Spanning sets
B.1 Unrestricted sumsets
B.1.1 Fixed number of terms
B.1.2 Limited number of terms
B.1.3 Arbitrary number of terms
B.2 Unrestricted signed sumsets
B.2.1 Fixed number of terms
B.2.2 Limited number of terms
B.2.3 Arbitrary number of terms
B.3 Restricted sumsets
B.3.1 Fixed number of terms
B.3.2 Limited number of terms
B.3.3 Arbitrary number of terms
B.4 Restricted signed sumsets
B.4.1 Fixed number of terms
B.4.2 Limited number of terms
B.4.3 Arbitrary number of terms
C Sidon sets
C.1 Unrestricted sumsets
C.1.1 Fixed number of terms
C.1.2 Limited number of terms
C.1.3 Arbitrarv number of terms
C.2 Unrestricted signed sumsets
C.2.1 Fixed number of terms
C.2.2 Limited number of terms
C.2.3 Arbitrary number of terms
C.3 Restricted sumsets
C.3.1 Fixed number cfterms
C.3.2 Limited number cf terms
C.3.3 Arbitrary number cf terms
C.4 Restricted signed sumsets
C.4.1 Fixed number of terms
C.4.2 Limited number of terms
C.4.3 Arbitrary number of terms
D Minimum sumset size
D.1 Unrestricted sumsets
D.1.1 Fixed number of terms
D.1.2 Limited number of terms
D.1.3 Arbitrary number of terms
D.2 Unrestricted signed sumsets
D.2.1 Fixed number of terms
D.2.2 Limited number of terms
D.2.3 Arbitrary number cf terms
D.3 Restricted sumsets
D.3.1 Fixed number of terms
D.3.2 Limited number of terms
D.3.3 Arbitrary number of terms
D.4 Restricted signed sumsets
D.4.1 Fixed number of terms
D.4.2 Limited number of terms
D.4.3 Arbitrary number of terms
E The critical number
E.1 Unrestricted sumsets
E.1.1 Fixed number of terms
E.1.2 Limited number of terms
E.1.3 Arbitrary number of terms
E.2 Unrestricted signed sumsets
E.2.1 Fixed number of terms
E.2.2 Limited number cf terms
E.2.3 Arbitrary number of terms
E.3 Restricted sumsets
E.3.1 Fixed number of terms
E.3.2 Limited number of terms
E.3.3 Arbitrary number of terms
E.4 Restricted signed sumsets
E.4.1 Fixed number of terms
E.4.2 Limited number of terms
E.4.3 Arbitrary number of terms
F Zero-sum-free sets
F.1 Unrestricted sumsets
F.1.1 Fixed number of terms
F.1.2 Limited number of terms
F.1.3 Arbitrary number of terms
F.2 Unrestricted signed sumsets
F.2.1 Fixed number of terms
F.2.2 Limited number of terms
F.2.3 Arbitrary number of terms
F.3 Restricted sumsets
F.3.1 Fixed number of terms
F.3.2 Limited number of terms
F.3.3 Arbitrary number of terms
F.4 Restricted signed sumsets
F.4.1 Fixed number of terms
F.4.2 Limited number of terms
F.4.3 Arbitrary number of terms
G Sum-free sets
G.1 Unrestricted sumsets
G.1.1 Fixed number of terms
G.1.2 Limited number of terms
G.1.3 Arbitrary number of terms
G.2 Unrestricted signed sumsets
G.2.1 Fixed number of terms
G.2.2 Limited number of terms
G.2.3 Arbitrary number of terms
G.3 Restricted sumsets
G.3.1 Fixed number of terms
G.3.2 Limited number of terms
G.3.3 Arbitrary number of terms
G.4 Restricted signed sumsets
G.4.1 Fixed number of terms
G.4.2 Limited number of terms
G.4.3 Arbitrary number of terms
V Pudding
Proof of Proposition 2.2
Proof of Preposition 3.1
Proof of Preposition 3.4
Proof of Proposition 3.5
Proof of Preposition 4.2
Proef of Preposition 4.3
Proof of Theorem 4.4
Proof of Proposition 4.9
Proof of Proposition 4.10
Proof of Theorem 4.17
Procf of Proposition 4.22
Procf of Proposition 4.23
Proof of Proposition 4.26
Proof of Proposition 4.29
Proof of Proposition A.42
Proof of Theorem B.8
Proof of Proposition B.28
Proof of Proposition B.46
Proof of Proposition B.54
Proof of Proposition B.57
Proof of Proposition C.36
Proof of Proposition C.50
Proof of Proposition C.51
Proof of Proposition D.6
Proof of Theorem D.8
Proof of Theorem D.9
Proof of Theorem D.10
Proof of Theorem D.40
PIoof of Proposition D.42
Proof of Theorem D.47
Proof of Proposition D.59
Proof of Theorem D.72
Proof of Proposition D.128
Proof of Theorem E.15
Proof of Proposition E.76
Proof of Lemma E.87
Proof of Theorem E.100
Proof of Theorem E.108
Proof of Theorem E.109
Proof of Theorem F.6
Proof of Proposition F.27
Proof of Proposition F.28
Proof of Proposition F.32
Proof of Proposition F.35
Proof of Proposition F.46
Proof of Proposition F.80
Proof of Proposition F.83
Proof of Theorem F.88
Proof of Proposition F.116
Proof of Proposition F.156
Proof of Proposition F.179
Proof of Proposition G.22
Proof of Theorem G.27
Proof of Proposition G.64
Proof of Corollary G.65
Proof of Theorem G.67
Proof of Proposition G.73
Proof of Proposition G.74
Proof of Proposition G.82
Bibliography
Author Index
編輯手記
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