partitions Definition and 51 Threads

Hi there. Happy new year. I am interested in magic squares. I am particularly interested in how to fill a square of order n in a symmetrical and logical way by analyzing the possible ways to achieve a given sum of numbers. My question is about combinatorics analyses. For example for a square...

Hi, I am running on pc with 2 different Linux OS and the following partitions /dev/sda1 (Boot) /dev/sda2 (ArchLinux) /dev/sda3 (something empty) /dev/sdb1 (Ubuntu) /dev/sdb2 (EFI System partition) /dev/sdb3 (no name) Since I basically don't use ArchLinux, I wanted to uninstall it. I...

I have had enough with my Windows PC. I have decided to create a dual boot PC with Ubuntu 20.04 LTS. I am doing a dual-boot system because I need Windows for: Amazon prime video app MS office Here is a view of the partitions of the HDD: I have a lot of programs to install: MATLAB Android...

Homework Statement Show an example of a partition of the nonzero integers into two infinite sets. Show an example of a partition of the nonzero integers into infinitely many sets, such that each set of the partition contains exactly two elements. 2. Homework Equations The Attempt at a Solution...

I am trying to find all partitions of 10 into a sum with 6 terms. Apparently there are five, but I can only find four. 10=5+1+1+1+1+1 10=4+2+1+1+1+1 10=3+2+2+1+1+1 10=2+2+2+2+1+1 I honestly don't see how there can be another partition... EDIT: Nevermind... Found it...

Hello. Is it possible to create logical partitions for an external storage such as an SD Card? When I take a back up, I format the disk instead of deleting the old data because deletion takes too much time compared to formatting. Then I do a copy-and-paste new data to the disk evacuated from old...

If the Euclidean plane is partitioned into convex sets each of area A in such a way that each contains exactly one vertex of a unit square lattice and this vertex is in its interior, is it true that A must be at least 1/2? If not what is the greatest lower bound for A? The analogous greatest...

Homework Statement Show that every partition of X naturally determines an equivalence relation whose equivalence classes match the subsets from the partition. Homework Equations ( 1 ) we know that equivalence sets on X can either be disjoint or equal The Attempt at a Solution Let Ai be a...

Homework Statement Find a recursive relation on the number of partitions ##P_n## for a set ##S_n## of cardinal ##n##. ##P_0 = 1## is given. Homework EquationsThe Attempt at a Solution A partition of ##S_{n+1}## is given by the choice of a non-empty ##k##-block ##A_k## of ##S_{n+1}## and a...

If someone could explain some of the steps needed to work out these 2 questions it would be much appreciated!

Hi, I am doing self study of Abstract Algebra from Pinter. My doubt is regarding Chap 13 Counting Cosets: A coset contains all products of the form "ah" where a belongs to G and h belongs to H where H is a subgroup of G. So each coset should contain the number of elements in H. Now the number of...

Homework Statement "A family of sets is called pairwise disjoint if any two distinct sets in the family are disjoint". so if ANY of the two sets are disjoint with each other then the whole family can be called pairwise disjoint.. "If A is a nonempty set, a family P of subsets of A is...

i don't have a specific question. i just need an explanation on what this topic is about. i am not understanding it

Hi! :) I am looking at the following exercise: Let $f:[a,b] \to \mathbb{R}$ integrable at $[a,b]$,such that $f(r)=0$,for each rational number $r \in [a,b]$.Prove that $\int_a^b f(x) dx=0$. We suppose the partition $P=\{ a=t_0<t_1<...<t_n=b\}$ of $[a,b]$ $\underline{\int_{a}^{b}} f(x)dx=sup \{...

So my textbook asks to show \int^{3}_{1} x^{2}dx = \frac{26}{3}. They let the partition P = {x_{0},...,x_{n}}, and define the upper Riemann sum as U(P) = \sum^{i=1}_{n} x_{i}Δx_{i} and lower sum as L(P) = \sum^{i=1}_{n} x_{i-1}Δx_{i} I understand this part, but the next part is where I'm...

Define a partition of a set $S$ as a collection of non-empty disjoint subsets $\in S$ whose union covers $S$. The number of them is defined using the Bell numbers. Can we define ''Non-crossing'' partitions in words . I have seen the visualization of these partitions and the number of them is...

1. If you had 10, 50, 20, 30, and 60 KB in order and wanted to work with these incoming processes 21, 47, 5, 45 KB find the best fit. 3. I know how to do 21 and 5 but for 47 and 45 I'm confused. Best fit says to produce the smallest left over hole. So, would I put 47 in 60 because it's...

Very much a beginner in maths and broadening my horizons. I have a series of polynomials that I was hoping to get some insight into, specifically where to beginning looking re. a method of creating a generating function, as well as some self similar patterns and links that explain them. Any help...

I have been investigating goldbach partitions for some time. One interesting observation I have been able to determine is concerning the "direction" of the goldbach partitions whether they are increasing or decreasing as 2N increases. To get an idea of this I constructed a function f(2N)...

Homework Statement If I had a recurrence expression that recurs on partitions of size n - 1 each time, (as opposed some fraction of the original size ie. n/2), how can I apply the Master Theorem? I don't know what the "b" value is? Homework Equations The Attempt at a Solution...

Hi All; The following attachment shows a diagram of the ratio R[2m] = g^2[2m]/g[2m-2]*g[2m+2] where g[2m] is the number of goldbach partitions for the even number 2m. What is the reason for the "forbidden zones". I understand this is somehow to do with the factors of the even number...

After long and careful search on the web and in literature, I could not find the solution of the following problem. I need calculate p(N,K,L) - the number of partitions of N into no more than K parts not exceeding L. Example: N = 7, K = 4, L = 5 1) 2+5 2) 3+4 3) 1+1+5 4) 1+2+4 5) 1+3+3 6)...

I noted the following concerning the cumulative sum of Goldbach partitions C[2N] = sum[ G(2N) ;from 6 to 2N] is greater than pi[2N]*(pi[2N] -1)/2 where 2N is an even number 2N=6,,,,, C[2N] is the cumulative sum of the goldbach partitions of the even numbers 6,...2N G(2N) is the...

Let A be the set of all functions f:{1,2,3,4,5}->{1,2,3} and for i=1,2,3 let Ai denote a subset of the functions f:{1,2,3,4,5}->{1,2,3}\i. i)What is the size of : 1). A, 2).the sizes of its subsets Ai,and 3).Ai\capAj (i<j) also 4).A1\capA2\capA3. ii)Find with justification the...

Homework Statement Let T_{n} denote the number of different partitions of {1,2,...,n}. Thus, T_{1} = 1 (the only partition being {1}) and T_{2} = 2 (the only partitions being {1,2} and {1},{2}). show that T_{n+1} = 1 + \sum^{n}_{k=1} (^{n}_{k}) T_{k}. Homework Equations Let S be a given...

Homework Statement Suppose A_{\lambda}, \lambda in L, represents a partition of the nonempty set A. Define R on A by xRy <=> there is a subset A{\lambda} such that x is in A{\lambda} and y is in A{\lambda}. Prove that R is an equivalence relation on A and that the equivalence classes of R are...

This problem is from Hrbacek and Jech, Introduction to Set Theory, Third Edition, right at the end of chapter 2. Homework Statement Let A \neq {}; let Pt(A) be the set of all partitions of A. Define a relation \leq in Pt(A) by S_{1} \leq S_{2} if and only if for every C \in S_{1}...

Intuitive reasoning has led me to develop a simple approximation, which contains factors different from those used in well knoen formulas. Numerically, "my" formula delivers results, which are almost as accurate, as Hardy-Littlewood`s with the Shah-Wilson correction. Thanks in advance for any...

The number of partitions of an even number 2N into N parts appears to be equal to the number of partitions of N. Is this known? If so: Can anyone provide a reference of the corresponding proof? Thanks in advance for any information on this.

Homework Statement I'm currently trying to revise for exams and really struggling on this problem: Suppose you have 3 coins that look identical (ie don't know which is which) with probabilites of 1/4, 1/2 and 3/4 of showing a head. 1. If you pick a coin at random and flip it, what is...

Well the questions and solutions are in one for some and I will type out the rest. Q6 http://img249.imageshack.us/img249/2757/47026197.jpg Q4 http://img237.imageshack.us/img237/1802/93774799.jpg Q3 http://img3.imageshack.us/img3/5919/34981698.jpg Q1...

I was given a problem where I was to find two disjoint partitions, S_1 and S_2 and a set A such that |A| = 4 and |S_1| = 3 and |S_2| = 3. Now the set I was using and the book eventually used was A = {1,2,3,4} and S_1 = {{1},{2},{3,4}} and S_2 = {{1,2},{3},{4}}. The question I have is probably...

If I have a semigroup S, is it possible to partition the set of element S into two semigroups S_1 and S_2 (with S_1 \cap S_2 = 0), in such a way that S_1 has an identity element but S_2 has none?

please can u help me ? IN Windows environment : 1- what is the max. no. of partitions that can be made ? 2- why always the color of any folder is yellow ? 3- what is the max. length of the name of the folder ? 4- why there is no partition named B ? thx

This is causing me a bigger headache than I anticipated. Basically, given an integer N and a number M, I need a list of all the possible integer partitions of N into M parts such that each part is strictly positive and each part is UNIQUE. I don't want repetitions. Just unique ones. So for...

Homework Statement Let f(x) = x, x \in [0,1], P_{n} = {0, \frac{1}{n}, \frac{2}{n},..., \frac{n}{n} = 1}. Calculate U_{P_{n}}(f) and L_{P_{n}}(f). Homework Equations U_{P_{n}}(f) is the sum of the upper partitions and L_{P_{n}}(f) is the sum of the lower partitions. A hint was...

[SIZE="2"]Homework Statement Suppose f:[a,b] \rightarrow \Re is bounded and that the sequences {U_{P_{n}}(f)}, {L_{P_{n}}(f)} are covergent and have the same limit L. Prove that f is integrable on [a,b]. [SIZE="2"]Homework Equations U_{P_{n}}(f) is the upper sum of f relative to P, and...

in my readings, spivak or elsewhere, I've come across this several times but i don't have the formal training (maturity) to know how to use it. intuitively: by the atlas maps on the manifold, we can chop up a manifold into patchs. for each patch, by smoothness or something, there is a smooth...

How many ways can you place 10 identical balls into 3 identical boxes? Note: Up to two boxes may be empty. I approached this problem as: Let B represent ball Let 0 represent nothing (empty) |box wall| 0 0 B B B B B B B B B B |box wall| So, there must be two other box walls that...

Homework Statement (proof) Determine whether or not (x,y)~(w,z) if and only if y=w is an equivalence relation. If it is, then describe the associated partition. Homework Equations The Attempt at a Solution Let x be an element of the reals. It is known that a relation on a set X...

Hi Is there a relatively easy way to calculate the number of partitions of a number given the maximum term and the count of terms? A couple of examples: 25 has four partitions with five terms where each term is unique and the largest term is 8 {8,6,5,4,2} {8,7,5,3,2} {8,7,5,4,1} {8,7,6,3,1}...

Does anyone do these? Sudoku is based on magic squares, Kakuro is based on partitions of integers. I haven't really tried solving any yet but my first impression was that Kakuro is generally tougher than Sudoku (for me anyway). http://en.wikipedia.org/wiki/Kakuro

what are they exactly?

With several partitions on a HD, if I move all the files from one partition to another, then back, doesn't that equate to a defragmentation? Strange question, I know.

Hi I need help with this problem I have some trouble with partitions: Homework Statement The context is Discrete math /relation Which of these collections of subsets are partitions of the set of integers? 1- The set of even integer and the set of odd integers. 2- the set of...

Not really homework, but something that our professor asked us the other day. Here is the question (I think): Let S be a set with #S=8. Find the number of partitions of S with equal length. ------- That probably makes no sense, namely the equal length part, so let me elaborate. Note: Let P be...

http://en.wikipedia.org/wiki/Integer_partition The above link should set the context. Given an integer q, the total number of partitions is given by partition function p(q). For example, 4 = 4 = 3+1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1 So, p(4) = 5. In mathematica, one can...

Problem: "Let G be a group of permutations of a set S. Prove that the orbits of the members of S constitute a partition of S." I'm a little hazy on how to start this proof. I started by writing down the definition of the Orbit of any element in S. I'm guessing, so correct me if I'm...

Im kind of lost here can somebody help me out please! Let S = {a, b, c, d} and let P = { {a}, {b,c}, {d} }. Note that P is a partition of S. Describe the equivalence relation R on S determned by P. This is a weird question that came out of my textbook. I know what a set is, and a...

This question probably falls more in the philosophical arena than the practical, but I didn't see any available "math philosophy" forums, so here goes. I've always found it curious why, out of all the possible ways to partition a number, is standard division a/b considered "natural." That is...