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
Permutations
8
Permutations
9
Visual representations of permutations
10
Generators
11
Sign of a Permutation
12
Inversions
13
Exercises
Generating Functions
14
Weight Functions
15
Generating Functions
16
Multiplication of Generating Functions
17
Stars and Bars Revisited
18
Coefficient Extraction
19
Exercises
Regular Languages
20
Regular Languages
21
Finite Automata
22
Putting Everything Together
23
Transfer Matrix Method
24
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