Looking for intro combinatorics/discrete math book with the following topics

In summary, the conversation discusses various topics in discrete mathematics, including binary strings, strings over arbitrary alphabets, generating functions, and their applications to enumeration and probability problems. Recommendations for related books are also provided, including Concrete Mathematics by Knuth and friends, and Automata, Computability, and Complexity by Elaine Rich. The speaker expresses interest in problems involving strings over arbitrary alphabets and generating functions, such as finding the average number of blocks in a string of a given length. However, there is a lack of introductory combinatorics books that cover this specific type of problem.
  • #1
Werg22
1,431
1
1. A discussion of binary strings and strings over arbitrary alphabets
2. A discussion of generating functions and bivariate (or multivariate) generating functions, and their applications to enumeration and and probability problems
3. Graphs and Trees (does not need to be that thorough for this part)

Any recommendation?

Thanks in advance.

Edit:

Posted in the wrong section - should be moved to Science Books Discussion
 
Last edited:
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  • #2
For discrete math in general there's Knuth and friend's Concrete Mathematics. For generating functions there's http://www.math.upenn.edu/~wilf/DownldGF.html" , which you can download from the author's website. I suppose if you're interested in binary strings and such you'll want to get into formal languages, automata, etc. My class is using Automata, Computability, and Complexity by Elaine Rich. I don't know if you'll find an intro book that covers all those things you listed. Is there something particular you're interested in?
 
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  • #3
I'm mainly interesting in problems involving any kind of strings (over arbitrary alphabets, not just binary), problems generally involving generating functions. For example, I'm interested in seeing how a problem of the like "find the average number of blocks of length 2 among all strings of length 10 over an alphabet of 4 letters {a, b, c, d}", this sort of thing. But from what I've seen so far, there aren't any introductory combinatorics book that look at this type of problem.
 

Related to Looking for intro combinatorics/discrete math book with the following topics

1. What is Combinatorics/Discrete Math?

Combinatorics and Discrete Math are branches of mathematics that deal with counting, arranging, and organizing objects or events in a systematic way.

2. What topics are typically covered in an introductory Combinatorics/Discrete Math book?

An introductory Combinatorics/Discrete Math book will typically cover topics such as basic counting principles, permutations and combinations, graph theory, and probability.

3. What is the importance of studying Combinatorics/Discrete Math?

Combinatorics/Discrete Math has practical applications in fields such as computer science, engineering, and economics. It also helps develop critical thinking and problem-solving skills.

4. Are there any specific prerequisites for studying Combinatorics/Discrete Math?

A basic understanding of algebra and mathematical reasoning is helpful for studying Combinatorics/Discrete Math. Some books may also require knowledge of calculus.

5. Can you recommend any specific books for learning Combinatorics/Discrete Math?

Some popular introductory books on Combinatorics/Discrete Math include "Concrete Mathematics" by Ronald Graham, "Discrete Mathematics" by Kenneth Rosen, and "A Walk Through Combinatorics" by Miklós Bóna.

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