Questions on discrete mathematics generally: "the study of mathematical structures that are fundamentally discrete rather than continuous"
0
votes
2answers
116 views
How do you prove this theorem?
Let:
A = { 1, 3, 9, 27, 81, 243, 729 }
B = { 1, 3, 9, 27, 81, 243, 729 }
C = some combination of A ($7$ Choose $k$ where $k= 0$ to $7$)
D = some combination of B ($7$ choose $k$ where $k= 0$ to ...
0
votes
2answers
32 views
Combinatorics question
A person can feel the four basic flavors: sour, sweet, salty, bitter. Any different flavor is Combination of some of the flavors mentioned above.
How much different falvors we have in total?
How ...
0
votes
2answers
24 views
How many functions Injective have for $|A|=3 \rightarrow |B|=4$ And How many Surjective
How many functions Injective and Surjective have for $|A|=3 \rightarrow |B|=4$
for example :
$$A=\{1,2,3\} \rightarrow B=\{1,2,3,4\}$$
the answer for Injective is: $4\cdot 3 \cdot 2$ or $\binom {3} ...
0
votes
3answers
44 views
$A=\{1,2,3,4,5\}$, $B=\{1,2\}$ How many functions $f:A\rightarrow B$ exists
I`m trying to calculate how much functions there is for $A=\{1,2,3,4,5\}$, $B=\{1,2\}$ that
$f:A\rightarrow B$
I know that $f(a_{i})=y\in B $ and only one from A, but there is two option the first ...
1
vote
1answer
38 views
Combinatorics Question with limitations
$n$ men $\rightarrow n \in N$
$n$ women $\rightarrow n \in N$
$n$ childs $\rightarrow n \in N$
How many ways we can order them:( lets say in row )
without limit
1 man and 1 woman can`t sit ...
1
vote
0answers
9 views
Mapping Reduction for Language?
If I have a language D = {M | M is a decider}, which is the language of turing machines that are deciders, how can I give a mapping reduction from D to $A_{All}$ where
$A_{All}$ = {M | M is a TM and ...
1
vote
0answers
33 views
Using discrete calculus to study convergence of series and sequences
From some personal investigation, I've noticed that all convergence tests for infinite series (at least, the real kind) can be rephrased in terms of the discrete derivative $∆f(x)$ of a function ...
2
votes
1answer
27 views
Subset product series
I have the following series:
S3 = 1/1 + 1/2 + 1/3 + 1/1*2 + 1/1*3 + 1/2*3 + 1/1*2*3
The question is to find a formula to produce this series (Sn)
I'm kinda stuck here. I know you can determine the ...
0
votes
4answers
28 views
How do I derive a characteristic equation for this specific recurrence relation?
I have no problems solving recurrence relations with two roots, but I've just encountered one with one root: $c_{n+1} = 3c_{n}+1$ such that $c_{0} = 0$.
In my solving process, I suppose I've gotten ...
0
votes
2answers
30 views
Recurrence relations for $a_{n+2}$
I'm trying to figure out how to find closed form equations for recurrence relations. I can find lots of examples for solving equations such as $a_{n} = ca_{n-1} + ca_{n-2}$ and $a_{n+1} = ca_{n} + ...
1
vote
0answers
45 views
How do I generate numbers like these?
In Matlab I can generate a 2d uniform grid with the following:
size = 300;
for (i=1:size)
x(i)=i/size;
y(i)=(size-i)/size;
plot(x,y,'.');
end
How do I ...
0
votes
2answers
20 views
Variance of n Bernoulli Trials
Count the variance of n Bernoulli trials with each probability of success is p.
Let random variable $X_i$ be
$1$ if trial is success, or
$0$ if trial fails.
Then expected value $E(X_i) = 1 ...
2
votes
1answer
36 views
polynomials over finite field with irreducible factors of odd degrees
It is well-known that the number of monic $n$-degree polynomials over a finite field of size $q$ is $q^n$. How many such degree-$n$ polynomials can be completely factored into only irreducible ...
9
votes
1answer
236 views
+200
How to justify the solution of this problem?
Assume $\mathbf{x} \in \mathbb R_+^N$ with support $P=\{p_1,p_2,\cdots,p_K\}$ ($P$ is unknown).
We already know that $$f_1(\mathbf{x}) = f_2(\mathbf{x}) = \cdots = f_{N-1}(\mathbf{x})$$
where
...
1
vote
3answers
33 views
Finding unknown values from discrete probabilities.
(I am confused here with the limits. It says x = 0,1,2,3... So what is my end limit her? Thanks.)