# Questions tagged [discrete-mathematics]

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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### Inverse of a circulant matrix via DFT

I am trying to do some practice in computing the inverse of a circulant matrix via the formula Inverse of a circulant matrix. I got that the first row of the inverse is \label{a}\begin{...
• 45
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### If we choose a line segment at random, then what is the expected number of paths that pass through it?

I was trying to solve this question. To find the expected number of paths that pass through a randomly chosen line segment: I observed that for different line segments the probability is different. Do ...
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### Find $K_r$-subdivisions in random graphs

I saw the following exercise in Shapira's note, page 22-23. Prove that with high probability, $G(n,1/2)$ does not contain a $K_t$-subdivision (also called topological minor) with $t=10\sqrt n$, but ...
• 343
1 vote
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### Derive Centerpoint theorem from Helly's theorem

Helly's theorem : Let $C_1,\ldots,C_n$, $n\geq d+1$, be convex sets in $\Bbb R^d$. Suppose every $d+1$ have a common intersection. Then they all have a common intersection. Proof: We're given that ...
• 306
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### How to Arrange 21 Uniquely Sized Squares to Form a Perfect Square?

I’m tackling a geometric puzzle where I have 21 squares, each with a different integer side length. The goal is to arrange these squares so that they perfectly fill a larger square without leaving any ...
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### What are the preferred steps to solve an exercise that involves finding all possible combinations/solutions for a string with constraints?

I have an exercise divided in two parts: a.) How many ( $x \in \mathbb{Z}$ ), with ($104050607080 \leq x \leq 908070605040$ ), can be formed using the digits of ( $106506506503$ ), such that ( $x$ ) ...
• 141
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### Nested Mathematical Induction [closed]

I have a result saying that "for all $s\geq 7$ and for all $V_J=\{v_{5j+1},v_{5j+2},v_{5j+3},v_{5j+4},v_{5j+5}\}$ for $J=j \in \{0,1,2, \cdots,\lfloor{\frac{s}{5}}\rfloor\}$, the property $P$ is ...
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### Finding non-repeating 9-digit numbers [closed]

Suppose that you are asked to find out a 9-digit number, consisting of numbers from 1 to 9 without repeating. Each time you may initiate a guess attempt of the number, and you will get a value of how ...
1 vote
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### Steps on solving point to plane exercises

I just want confirmation that the steps I've took to solve these two exercises are correct Exercise 1 Consider in R3 the line $l$ defined by: \begin{cases} x = 2 + 3t \\ y = 2 - 2t \\ z = 1 + t \\ t \...
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### Binomial identity involving square binomial coefficient [closed]

I want to prove this identity, but I have no idea... Could someone please post a solution? Thank you. $$\sum_{k=0}^{n} \binom{-1/2}{n+k}\binom{n+k}{k}\binom{n}{k}= \binom{-1/2}{n}^2$$ (Maybe -1/2 can ...
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### Show that $\sum_{k=1}^n{2^{2k-1}\binom{2n+1}{2k}B_{2k}(0)}=n$

Lately, I've been working on a proof (whose context is not necessary to discuss) and I only need one last thing in order to finish it. To be more specific, for completeness it would suffice to show ...
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### Column/Digit blind solution for the "Number of possible combinations of x numbers that sum to y"

What formula will give me "the total number of possible combinations of x digits that sum to y". This is a branch question from the original question entitled Number of possible ...
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### Regarding the question of translating the verbal descriptions of definitions and theorems into propositional logic

I am studying discrete mathematics and recently trying to describe mathematical definitions or theorems in the form of propositional calculus or predicate calculus. I am not sure if my approach is ...
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