Notation 
1. 
Introduction and Sperner's theorem 

1.1 
A simple intersection result 

1.2 
Sperner's theorem 

1.3 
A theorem of Bollobás 


Exercises 1 
2. 
Normalized matchings and rank numbers 

2.1 
Sperner's proof 

2.2 
Systems of distinct representatives 

2.3 
LYM inequalities and the normalized matching property 

2.4 
Rank numbers: some examples 


Exercises 2 
3. 
Symmetric chains 

3.1 
Symmetric chain decompositions 

3.2 
Dilworth's theorem 

3.3 
Symmetric chains for sets 

3.4 
Applications 

3.5 
Nested Chains 

3.6 
Posets with symmetric chain decompositions 


Exercises 3 
4. 
Rank numbers for multisets 

4.1 
Unimodality and log concavity 

4.2 
The normalized matching property 

4.3 
The largest size of a rank number 


Exercises 4 
5. 
Intersecting systems and the ErdösKoRado theorem 

5.1 
The EKR theorem 

5.2 
Generalizations of EKR 

5.3 
Intersecting antichains with large members 

5.4 
A probability application of EKR 

5.5 
Theorems of Milner and Katona 

5.6 
Some results related to the EKR theorem 


Exercises 5 
6. 
Ideals and a lemma of Kleitman 

6.1 
Kleitman's lemma 

6.2 
The AhlswedeDaykin inequality 

6.3 
Applications of the FKG inequality to probability theory 

6.4 
Chvátal's conjecture 


Exercises 6 
7. 
The KruskalKatona theorem 

7.1 
Order relations on subsets 

7.2 
The lbinomial representation of a number 

7.3 
The KruskalKatona theorem 

7.4 
Some easy consequences of KruskalKatona 

7.5 
Compression 


Exercises 7 
8. 
Antichains 

8.1 
Squashed antichains 

8.2 
Using squashed antichains 

8.3 
Parameters of intersecting antichains 


Exercises 8 
9. 
The generalized Macaulay theorem for multisets 

9.1 
The theorem of Clements and Lindström 

9.2 
Some corollaries 

9.3 
A minimization problem in coding theory 

9.4 
Uniqueness of a maximumsized antichains in multisets 


Exercises 9 
10. 
Theorems for multisets 

10.1 
Intersecting families 

10.2 
Antichains in multisets 

10.3 
Intersecting antichains 


Exercises 10 
11. 
The LittlewoodOfford problem 

11.1 
Early results 

11.2 
Mpart Sperner theorems 

11.3 
LittlewoodOfford results 


Exercises 11 
12. 
Miscellaneous methods 

12.1 
The duality theorem of linear programming 

12.2 
Graphtheoretic methods 

12.3 
Using network flow 


Exercises 12 
13. 
Lattices of antichains and saturated chain partitions 

13.1 
Antichains 

13.2 
Maximumsized antichains 

13.3 
Saturated chain partitions 

13.4 
The lattice of kunions 


Exercises 13 

Hints and solutions; References; Index 