Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West (University of Illinois, Urbana).
I have a doubt about the notation and alternative ways to represent the terms involved in sums.
Suppose that we have the following multivariable function,
$$f(x,y)=\sum^{m}_{j=0}y^{j}\sum^{j-m}_{i=0}x^{i+j}$$.
Now, let ##\psi_{j}(x)=\sum^{j-m}_{i=0}x^{i+j}##. In the light of the foregoing, is...
I submitted this solution, and it was marked incorrect. Could I get some feedback on where I went wrong?
Let S represent the event that Party A wins the senate and H represent the event that Party A wins the house.
There are 4 cases: winning the senate and house (##S \cap H##), winning just...
I need to show the following thing: Given a collection of 5 rays (half-lines) in the plane, show that it can be partitioned into two disjoint sets such that the intersection of the convex hulls of these two sets is nonempty.
Attempt - I am stuck at this problem for hours, couldn't make any progress. Still, here's what I've done :
Let ## e_1 \in E_1 \setminus E_2 ## be arbitrary. Suppose for the sake of contradiction that ## \forall ## ## e_2 \in E_2 \setminus E_1 ##, ## T_1' = \langle V,(E_1\setminus \{ e_1 \})...
Here's a math question I've been thinking about lately.
We have a stick of length one which is broken in one spot (with that spot chosen randomly and uniformly). Of the two broken pieces we take the one on the right and break it into two pieces in the same manner as before.
With our three...
Sorry in advance if I've posted in the wrong section.
given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}##
where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##
How would you go about finding the bounds of something like this, or determining if it even has any?
##( \...
I have been studying discrete mathematics for fun and I am kind of stuck on this bijection problem.
1. Homework Statement
I wanted to apologize in advance if i put this homework question in the wrong part of the forums. Discrete Math and much logic math is a computer science type math of...
To prove that n log n is big oh of log(n!), I did:
n log n <= C log(n!)
n log n/ log(n!) <= C
Let k = 1
n > k, so for n = 2
2 log 2 / log 2 <= C
2 <= C
C is an element of [2, infinity)
Taking C = 2 and k = 1
can we say, n log n <= 2 log(n!)
and hence n log n is big oh of log(n!) ?
Hi guys,
I have functioning MATLAB code for my solution of the 3D Diffusion equation (using a 3D Fourier transform and Crank-Nicolsen) that runs just from the command window and automatically plots the results. However, it seems like my solution just decays to zero regardless of what initial...
my attempt.
Let P = At least one a and at least one b
Let Q = r=a/b
Hence the proposition is simplified to,
For all r where P Then Q
Negation:
Not all r where P Then Q
= Atleast one R When Not(P Then Q)
Not(P Then Q) = P And Not Q
Hence
Atleast one R When Not(P Then Q)
= Atleast one R When...
Hi all,
Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject?
Thanks!
<<Mentor note: Missing template due to originally being posted in other forum.>>
So, my professor gave a problem which stated:
Given a 15 x 20 rectangle, prove that if 26 points are chosen, at least one pair will be at most five units away.
What I said was to split the rectangle into 12 5x5...
Homework Statement
How many ways can you select 10 jellybeans from colors Red, Blue, Green so that at most you only have 4 Green jellybeans?
Homework Equations
...
3. The Attempt at a Solution [/B]
# of ways = # of ways to pick 1 Green + # of ways to pick 2 Green + #of ways to pick 3...
< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
(A+B)&(C+D) + (A+B)&(C+D)' + C
(A+B)&(C+D) + (A+B)&(C'&D') + C by deMorgans
(A+B)&[(C+D)+(C'&D')] + C by Distributive
I'm just wondering if I did anything wrong in this simplification or if it...
Hi everyone,
I haven't been successful in Discrete Math this semester. I have finished all of the calculus I-III series and I did very well. I want to know if anyone can give me some tips on how to study for my final coming up in a few days.
Now, I understand that is a vague question but I am...
Homework Statement
Let A=RxR=the set of all ordered pairs (x,y), where x and y are real numbers. Define relation P on A as follows: For all (x,y) and (z,w) in A, (x,y)P(z,w) iff x-y=z-w
Homework Equations
R is reflexive if, and only if, for all x ∈ A,x R x.
R is symmetric if, and only if, for...
Prove the following theorem:
Theorem For a prime number p and integer i,
if 0 < i < p then p!/[(p− i)! * i] * 1/p
Not sure how to go about this. I wanted to do a direct proof and this is what I've got so far.
let i = p-n
then p!/[(p-n)!*(p-n)] but that doesn't exactly prove much.