|
- What is combinatorics? - Mathematics Stack Exchange
In fact,I once tried to define combinatorics in one sentence on Math Overflow this way and was vilified for omitting infinite combinatorics I personally don't consider this kind of mathematics to be combinatorics, but set theory It's a good illustration of what the problems attempting to define combinatorial analysis are
- What is the difference between combinatorics and discrete mathematics . . .
So if "combinatorics is a subset of discrete mathematics" should indeed be true: I would like to see a concrete example of a subject being discrete math, but not combinatorics I was a bit surprised to find that the (oldschool?) viewpoint "combinatorics = counting" is also suggested by our MSE tag descriptions
- Book recommendations for Combinatorics for Computer Science Students
Could anyone recommend comprehensive books or resources on combinatorics that are particularly suited for computer science students? Ideally, these resources would cover both fundamental concepts and advanced topics, with applications to algorithm challenges
- Olympiad Combinatorics book - Mathematics Stack Exchange
Can anyone recommend me an olympiad style combinatorics book which is suitable for a high schooler ? I know only some basics like Pigeon hole principle and stars and bars I hope to find a book w
- reference request - Undergrad-level combinatorics texts easier than . . .
I am an undergrad, math major, and I had basic combinatorics class using Combinatorics and Graph Theory by Harris et al before (undergrad level) Currently reading Stanley's Enumerative Combinatorics
- combinatorics - Formula for Combinations With Replacement - Mathematics . . .
I understand how combinations and permutations work (without replacement) I also see why a permutation of n n elements ordered k k at a time (with replacement) is equal to nk n k Through some browsing I've found that the number of combinations with replacement of n n items taken k k at a time can be expressed as (\mathchoice((((n k\mathchoice))))) (\mathchoice ((((n k \mathchoice))))) [this
- Combinatorics: Bars and Stars Confusion - Mathematics Stack Exchange
Suppose we have $5$ stars and $2$ bars Assume that there can be multiple bars between the consecutive stars Then, there are $6$ possible spots for the bars, which should mean number of different
- combinatorics - Proving Pascals identity - Mathematics Stack Exchange
I know you can use basic algebra or even an inductive proof to prove this identity, but that seems really cumbersome I was wondering if anyone had a "cleaner" or more elegant way of proving it For example, I think the following would be a decent combinatorial proof Proof: Let S S be a set with n + 1 n + 1 elements, and consider some fixed x ∈ S x ∈ S There are (n+1 r) r (n + 1 r) r
|
|
|