# Tagged Questions

For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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### every tree $T$ has at most one perfect matching, alternative proof

I have two questions: I need to know if the following approach (by induction) is correct. The ones I saw use induction on the components of $T$ with a leaf removed, I did something a little different....
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### Josephus problem: the renumbering method from Concrete Mathematics

In Concrete Mathematics, Chapter 3, Section 3, an interesting method to solve the Josephus problem is discussed. The paragraphs below depict the method, which are extracted from the book: (Initially, ...
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### Combinatorics in a restaurant

In a restaurant menu there are 6 types of drinks : Coca cola , lemonade , sprite , wine , tea and diet sprite . How many people need to order a drink to ensure that at least one drink would be ...
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### Help in proof: a connected graph is $k$ edge connected iff all blocks are

Attempt: we know that the edge set of $G$ is the union of those of it's blocks (maximal connected subgraphs of $G$ not having a cut vertex), any two of them touching in at most one vertex. If all ...
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### Jessica the Combinatorics Student, part 2

The original question about Jessica, which I encourage review of, is as follows: Jessica is studying combinatorics during a $7$-week period. She will study a positive integer number of hours every ...
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### What is the coefficient of the following

I got the question on a midterm and got it wrong. I'd like to know where I went wrong. We were supposed to find the coefficient of $x^{15}$ of$$(1-x^2)^{-10}(1-2x^9)^{-1}$$ My answer The only way to ...
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### Supposedly really hard problem involving combinations

This problem gives 7 (max) out of 100 points for a college entrance exams. Seems odd because it looks easy to me, although my combinations are not too good. There are $10$ people forming a ...
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### Degree of Jacobian of homogeneous polynomials

What is the degree of the Jacobian (as a polynomial) of 3 homogeneous polynomials in 3 variables of degrees say $m_1, m_2$ and $m_3$ ? I don't know how to prove that it is independent. In my case the ...