Questions on discrete mathematics generally: "the study of mathematical structures that are fundamentally discrete rather than continuous"
1
vote
2answers
24 views
Inclusion & Exclusion: In how many permutations of the digits $0,…,9$ there's no continuity of 7 digits or more?
In how many permutations of the digits $0,...,9$ there's no continuity of 7 digits or more?
(Ex. the number 203456789 1 should not be counted)
I believe that the basic case, for the inclusion ...
1
vote
2answers
20 views
Let (a,b) and (c,d) be intervals on R, and find an injective and surjective function from (a,b) to (c,d)
so here is this question I got stuck on:
Let $(a,b)$, $(c,d)$ be intervals (not sure if that's the correct term) on $\Bbb R$, so that $a<b$, $c<d$. Find an injective and surjective function ...
1
vote
1answer
27 views
Combinatorics riddle: Sorting people in a cinema line.
Say i want to go to the cinema. There are two types of movies.
Action movie.
Drama movie.
Because action is more interesting it costs 50$. And the cost for drama is 10€.
There are 200 people ...
1
vote
2answers
34 views
Tree pruning question…
all. I'm facing the question:
"A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it ...
1
vote
0answers
36 views
Is discrete ultralogarithm harder than discrete logarithm?
Is computing $g^{xy} \bmod{s}$ from $g^{x} \bmod{s}$ and $g^{y} \bmod{s}$ easier harder or the same level of difficulty as computing
$g\uparrow\uparrow(xy) \bmod s$ from from $g\uparrow\uparrow x$ ...
0
votes
0answers
14 views
Modular Quadratic System of Equations
I have a system of quadratic equations of two variables to solve in several moduli:
$z_0 \equiv (x+k_0)^2-(x+k_0)y \ (mod\ n_0)$
$z_1 \equiv (x+k_1)^2-(x+k_1)y \ (mod\ n_1)$
...a
$z_m \equiv ...
4
votes
1answer
56 views
Is $AB+BA$ is positive definite too if $A$ and $B$ are positive definite?
I have a question: Is $AB+BA$ is positive definite too if $A$ and $B$ are positive definite matrices?
1
vote
1answer
28 views
8 friends, 7 nights, invite 4 every night, all of the friends must be invited, how many options?
Assume I have 8 friends, I want to invite 4 friends each night for 7 night so everyone will be invited at least once. How many combinations are there to do it?
I think I'm supposed to use the ...
0
votes
1answer
35 views
How many ways are there to sit $n$ couples on a bench when every couple sits together?
How many ways are there to sit $n$ couples on a bench with $2n$ sits, when every couple sits together?
How many ways are there to sit the couples so that none of the couples will sit together?
3
votes
2answers
44 views
Proving if a relation is an equivalence relation
I have been able to figure out the the distinct equivalence classes. Now I am having difficulties proving the relation IS an equivalence relation.
$F$ is the relation defined on $\Bbb Z$ as follows: ...
1
vote
3answers
41 views
Equivalence Relations: Equivalence Classes
From my basic understanding $R$ is an equivalence relation on the set $A$, which is
a relation between elements of a set that is reflexive, symmetric, and transitive.
I am not sure how to find the ...
2
votes
1answer
49 views
$\chi(G) \cdot \chi(\bar{G})\geq n$
Prove that $\chi(G) \cdot \chi(\bar{G})\geq n$
$\chi(G)$: number of colors required for a graph $G$.
Here $\bar{G}$ is a graph that consists of all the edges that are not in $G$.
0
votes
0answers
34 views
Discrete math: mathematical induction [duplicate]
Im having trouble doing this assignment with a given restriction
Show that n lines separate the plane into $\frac{n^2 + n + 2}{2}$
regions if no two of these lines are parallel and no three
pass ...
0
votes
1answer
13 views
Stability of nonlinear planar map fixed points.
Got the map:
$$x_{n+1} = x_ne^{2-x_n-y_n}$$
$$y_{n+1} = y_ne^{x_n-1}$$
I found the fixed points (0,0), (2,0), (1,1).
For the stability I have the Jacobian to find eigenvalues as:
$$J = ...
0
votes
2answers
56 views
Evaluating Line Integrals!
$3xy^2dx+2x^3dy$
where is the boundary of the region between the circles $x^2+y^2=25$ and $x^2+y^2=64$ having positive orientation.
Not quite sure how to evaluate this...
