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
Permutations
7
Permutations
8
Visual representations of permutations
9
Generators
10
Sign of a Permutation
11
Inversions
12
Exercises
Generating Functions
13
Weight Functions
14
Generating Functions
15
Multiplication of Generating Functions
16
Stars and Bars Revisited
17
Coefficient Extraction
18
Exercises
Regular Languages
19
Regular Languages
20
Finite Automata
21
Putting Everything Together
22
Transfer Matrix Method
23
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