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.
33,167
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FFT for the Estimation of Power Spectra (Welch's Method) - DFT Definition
I was reading Peter Welch's famous paper "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Aver. aging Over Short, Modified Periodograms" the ...
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This statement is false right? Susanna Epp Exercise Set 3.3, Question 19
Link to Question
Exist real number X, such that for every real number Y,X+Y = 0
This statement should be false right? The book did not tell us to show whether it ...
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Derive the closed-form expression of Delannoy Numbers
I am trying to derive the closed-form expression of Delannoy Numbers, as the one in the wikipedia: https://en.wikipedia.org/wiki/Delannoy_number#cite_note-7
The closed-form expression looks like this:...
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Reducing propositions using laws [closed]
Could someone help me to simplify nv(s^s) to n by using laws? I tried using all the laws that is available for this problem.
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Confusion on proof of a polynomial of degree n is $\Omega (x^n)$
This is a solution from Rosen's Discrete Math textbook for the problem of proving a polynomial of degree n is of order $x^n$, that is $\Theta(x^n)$.
I understand the proof for the polynomial of degree ...
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Finding a new MST for $G(V,E)$ after connecting a new vertex
Let $G(V, E)$ be an undirected, connected, graph. We have a weight function $w: E \to R$, and let $T$ be an MST of $G$.
Suppose we connect a vertex $v$ to $G$ with at least one edge, and let's call ...
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Generating MA Process in matlab using gaussian nosie
I have an MA process that is:
$x[n] = a * w[n] + b * w[n - 1] + c * w[n - 2]$
Where $a, b, c \in \mathbb{R}$ and $w \sim \mathcal{N}(0, \sigma^{2})$
How can I generate $x[n]$ in Matlab ?
I know that ...
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Given recurrence of $N_{n,m}$, how to find its upper bound
given recurrence $N_{n,m} = N_{n-1,m} + N_{n,m-1} + N_{n-1,m-1}$ with initial condition $N_{i,0} = 1, N_{0,j} = 1$, how to prove the upper bound of $N_{n,m}$ is $N_{n,m} \leq \frac{\{2(n+m)\}^n}{n!}$
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Question about concrete mathematics double summation derivation [closed]
How did the author in the image convert the summation into a double summation? I can see how the double summation turns into the sum of squared integers but how would you go about converting the sum ...
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How many $5$ or $6$-letter words can be created with $1$ a, $2$ b's, and $3$ c's?
How many $5$ or $6$-letter words can be created with $1$ a, $2$ b's, and $3$ c's?
I have calculated the number of permutations of all $6$ letters (all $6$-letter words) using $$\frac{n!}{n_1!n_2!n_3!} ...
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Is there a digraph with these 3 properties?
I'm wondering if there exists a digraph on the vertex set $\mathbb{Z}$ satisfying these conditions:
Each vertex has first outdegree equal to second outdegree (where second outdegree is the number of ...
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Help needed findint the expected value of this stopping time
Let $\xi_i$ be iid random variables with $\mathbb{E}[\xi_i]=0$, and define:
$$S_{(k)} = \sum_{i=1}^N \xi_{i+k}$$
Now, define:
$$\tau = \min \left\{ k : S_{(k)} \notin (a,b) \right\}$$
How can I find $\...
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exchange order of limit of random variable
Suppose to have a sequence of discrete random variables $X_n(\lambda)$ depending on some parameter $\lambda \ \in [0,\infty]$ and $n \in \mathbb{N}$ and that the following limits hold almost surely:
$...
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What do BFS trees tell use about their graph of origin
Let $G = (V, E)$ a connected graph. Let $\mathcal{B}_x(G) \subseteq G$ be the BFS tree with root vertex $x \in V$. Since $G$ is connected, $\mathcal{B}_x$ contains all vertices of $V$.
Informally, I ...
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This question requires the strong induction principle of propositional logic to be solved. [closed]
The principle of strong induction is a theorem equivalent to the principle of conventional induction, but sometimes it is more convenient to use strong induction to prove certain results. It can be ...
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