Combinatorics Notes
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Applied Combinatorics
Strings
4
Exercises
About
1
Preface
Trees
2
Trees
Strings
3
Forbidden Substrings
4
Exercises
Inclusion-Exclusion
5
Inclusion/Exclusion
6
Euler’s Totient Function
Stars and Bars
7
Stars and Bars
8
Upper bounds in Stars and Bars
Permutations
9
Permutations
10
Visual representations of permutations
11
Generators
12
Sign of a Permutation
13
Inversions
14
Exercises
Generating Functions
15
Weight Functions
16
Generating Functions
17
Multiplication of Generating Functions
18
Stars and Bars Revisited
19
Coefficient Extraction
20
Exercises
Regular Languages
21
Regular Languages
22
Finite Automata
23
Putting Everything Together
24
Transfer Matrix Method
25
Exercises
Strings
4
Exercises
4
Exercises
Find a recursive relation for
Binary strings that do not contain “100”
Ternary strings that do not contain “100”
Base-5 strings that do not contain “1234”
Ternary strings that do not contain “100” or “02”
3
Forbidden Substrings
5
Inclusion/Exclusion