Questions tagged [sets]

For questions pertaining to sets in the set-theoretical sense. Use "assignment" for questions about the use of the Mathematica functions Set or SetDelayed.

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34
votes
9answers
3k views

How to select minimal subsets?

I am a newbie, so please point me in the right direction if you feel this question has been answered somewhere else before. Here goes: Suppose I have a list like this: ...
20
votes
9answers
945 views

Any built-in function to generate successive sublists from a list?

Given lst = {a, b, c, d} I'd like to generate {{a}, {a, b}, {a, b, c}, {a, b, c, d}} but using built-in functions only, ...
18
votes
5answers
5k views

Define a mathematical set

I have a terribly short question: Is there a way to define a pure mathematical set? I tried a bit of googling, but the word "set" has two meanings and the other one (as in setting) as by far more ...
17
votes
8answers
1k views

Enumerating tuples from a larger space such that all pairs of values are present at least once

I am trying to write a function that will accept a list of N lists and returns a list of N-tuples that represent all pairs of values from the original N lists at least once. To illustrate with an ...
13
votes
3answers
2k views

how to efficiently apply function to all pairs of a set (and collect the results)

To build a graph, I need to apply a function f[a_, b_] to all pairs of a list (3500 elements). The function itself returns a link ...
12
votes
7answers
4k views

Combination and Permutation

How could I obtain the list of all the groups of 5 numbers taken from Range[12] such that the 2 lists have an empty intersection : ...
11
votes
10answers
1k views

Finding neighbors from list

Say you are given the following list: list={{3, 2, 1}, {3, 4, 2}, {2, 4, 1}, {1, 4, 3}}; Two numbers $x,y$, not necessarily distinct, are neighbors if one of the ...
11
votes
6answers
726 views

How to randomly select subsets

I have a list of around 300 elements. I want to sample subsets of length 25 such that my samples are all distinct. My first inclination was to use something like ...
11
votes
6answers
540 views

Performing Computations on Sets

I would like to find a permutation of $\quad S=\{\frac{1}{10}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{2}{3} \}\quad$ that maximizes the sum of theses elements raised to unique powers: $\;\{0,1,2,...
11
votes
4answers
478 views

Patternmatching sets

How to match set-patterns against sets? A set (in the mathematical sense) is a list of elements without repetition and order of elements does not matter. For example, we have a pattern set ...
10
votes
4answers
448 views

Delete sublist when sub-sublists contain same element

Given lis={{{a},{b,c,d}},{{a,b},{b,c}},{{b,c},{a,b,c}},{{b},{d}},{{a,b},{c,d}}} I want to delete sublists which have one or more elements in common. So that I ...
10
votes
4answers
630 views

Complement of multisets

Given lists $a$ and $b$, which represent multisets, how can I compute the complement $a\setminus b$? I'd like to construct a function xunion that returns the ...
10
votes
5answers
1k views

Subsets of a list

Consider the following demand of products for the next four months. data={1,20,3,40}; I could produce the whole demand in the first months, leading to the ...
9
votes
1answer
252 views

Is there an easy way to do set counting in Mathematica?

I'm using counts of elements in sets, along with logic. So, for instance, I'd like to determine if Count[$a \land \neg b$] = Count [$a$] - Count[$a \land b$] ...where ...
7
votes
5answers
486 views

Efficient deletion of specific list entries

It is sometimes useful to remove exactly the amount of specific entries on one list from another. Consider: ...
7
votes
2answers
192 views

Sets and sums of different elements

Consider the set S={w,x,y,z}. If the set of all possible sums of any three different elements from S is {-1,3,5,8}, then what is the set S? How could I solve this function using Mathematica?
7
votes
4answers
253 views

Finding largest Range in a list

In a list of positive integers, I would like to find the largest n such that Range[n] is a subset of the list. So for example ...
7
votes
1answer
279 views

How to get all possible orderings (equal ranks allowed) for given set of $N$ objects?

Hope there is a solution besides the tedious generation of nested loops. (Trying to avoid reinventing the wheel.) Here is an example with $N = 3$ objects. There are $13$ needed orderings (first ...
7
votes
1answer
355 views

A more perfect Union[]

I was doing a Project Euler problem with my class, and found the following weird fact: Union[] of a list of some 50 million numbers (of which only around 15000 were ...
6
votes
2answers
412 views

Get envelope of a set of functions?

I'm new with mathematica and I'm trying to solve a problem. I have a set of functions in the same variable. Let's say the domain is [0,2]. I would like to get an ordered list of the functions ...
5
votes
3answers
521 views

Is there a simple way to perform the opposite of intersection on two lists?

By "opposite of intersection" I mean that if I have two lists like so: list1 = {1,2,4,7,9}; list2 = {1,4,9,10,11} And then we do the "Reverse Intersection" on ...
5
votes
1answer
673 views

Intersection does not take list of lists

The function Intersection takes a number of lists (sets) and finds their intersection. However, the precise input is ...
5
votes
1answer
141 views

Amount of k-sized not-duplicated subsets of subsets of pair with disitinct sorted integers

I have a list, L, of this kind ($n\in \mathbb{N}$): L=Sort[RandomSample[Subsets[Range[n],{2}],RandomInteger[{1,Binomial[n,2]}]]] S contains any k-sized subset ...
5
votes
0answers
71 views

Looking for a package for finite mappings

I am looking for a package for dealing with "mappings" $f\colon A\to B$ where $A$ and $B$ are finite subsets of the set of all possible (inert) expressions. I need operations like: Computing $f(a)$ ...
4
votes
7answers
503 views

Concise way to generate multiset lists

I wrote the following to generate a multiset with the same number of items over a fixed range: ConstantArray[#, 3]& /@ Range[9] // Flatten ...
4
votes
2answers
1k views

Exact cover solution

Is it possible to get a exact cover solution(s) and/or number of possible solutions in Mathematica?
4
votes
1answer
285 views

List all possible elements of a set

I have this two sets: $A = \{\emptyset, \{\emptyset\}, \{\{\emptyset\}, \emptyset\}\}$ $B = \{\{x, \{x, y\}\} | x \in A, y \in A\}$ Now I want to list all possible elements that are in $B$. How do ...
4
votes
1answer
122 views

Non-flat partitions of a set

A non-flat partition of a set is one where, when the elements of the set are on a grid, the partition does not contain subsets with elements from the same row. When the set is more irregular the same ...
4
votes
2answers
145 views

How to constrain the generation of all possible orderings?

Here is code from Simon Woods' answer for getting all possible weak (equal ranks allowed) orderings for $N=3$ objects: ...
4
votes
3answers
79 views

every set intersection for every set in a family with another family of sets

I want to find for each list within a list of lists what intersections occur when taking set intersection for each list in another list of lists. Hopefully that makes sense. I have tried ...
4
votes
2answers
144 views

How can I define operators that implement the algebra of sets?

I need to define some operators with properties like idempotence and distribution over union and intersection so that Mathematica can symbolically simplify expressions. How do I define such operators? ...
4
votes
1answer
3k views

Putting set elements into venn diagram

My problem has two parts. Before that I have two Lists/Sets. It suppose to be created them by two initial strings. In the first part, I need to show sets' elements in venn diagram. I can create venn ...
3
votes
2answers
788 views

How to stretch this Venn diagram?

I am trying to duplicate (approximately) the following Venn diagram in Mathematica: I have used the top of this page as a guide, which showcases the following Venn diagram triplet: ...
3
votes
2answers
200 views

How to find the positions of replaced elements in a list

I have two sets of elements a={3, 4.8, 5, 4.2, 3.6, 2.3, 4.5, 3.7} b={2.8, 4.7, 5.3, 3.5, 4.7, 2.8, 4.2, 3.4} and I create ...
3
votes
1answer
2k views

How to make an efficient difference of sets function?

How to write a nice code that removes all elements from given set A, that occur also in set B? I would like to use DeleteCases[] for this purpose, but have no good ...
3
votes
2answers
1k views

How do I do the Minkowski sum of two sets?

I have 2 sets, $X$ and $Y$. How do I find the Minkowski sum of these sets?
3
votes
1answer
97 views

Why doesn't DeleteDuplicates do what I want

First off. I am not a mathematician I am a linguist, a syntactician who is trying to say something about semantics, which in the case at hand can be largely understood to reduce to set theory. That ...
3
votes
1answer
209 views

Finding pairs where the intersection of them is empty set from a nested list

It would be better to give an example first. Suppose I have a nested list of the form list = {{ 1,2,3,6}, { 3,6,10,20}, { 4,7,11}, { 10,20}}; where each element ...
3
votes
1answer
102 views

How can I create a set (list) provide a kind of rule/algorithm?

Example: S = {r ∈ Q : r² < 2} Let S be the set of all rational numbers whose squares are less than 2. It follows that 1 ∈ S, 4/3 ∈ S, but 3/2 doesn't ∈ S because 9/4 ≥ 2. Thank you.
3
votes
1answer
54 views

Eliminate from list of sets those that are equal (except for the order)

I have a list of sets and some of them are equal in the sense of mathematics, but are ordered differently. How can I remove those elements from my list? For example, the set ...
3
votes
0answers
706 views

How can I speed up my code which finds the ratio of two sums that are hard to compute? [closed]

Consider a set $\left\{\left. T(c, d)\right|c, d\in\mathbb{Z}\right\}$, a subset of the rational numbers. I want to compute $D$ $$D=\lim_{(a,b)\to(-\infty, \infty)}\lim_{(r, t)\to(\infty,\infty)}D'(...
3
votes
0answers
86 views

Listing all combinations produced by picking one element from each of several sets [duplicate]

I have a problem like this, I am given the following sets {a,b,c}, {d,e,f}, {h,i,j}. I want to pick one element from each set, and output a list of all the ...
2
votes
3answers
193 views

How to write equal subset

I have a unique set S={1,1,3,3,3} but from this unique set I can create many combinations like {1,3,3,3,1}, {3,3,1,3,1}, ... I ...
2
votes
2answers
3k views

Plot 3D set (or a domain of three-variable function)

is there any way to plot a "3D set" of points subject to certain rules? For example, my task is to find maximum of some function of three variables which have to meet some conditions. Of course I can'...
2
votes
2answers
1k views

Combining lists with common elements efficiently [duplicate]

Possible Duplicate: Computing the equivalence classes of the symmetric transitive closure of a relation I am required to process sets consisting of 2-element subsets of integers by combining ...
2
votes
2answers
106 views

Finding maximal elements of partially ordered sets

I am dealing with partially ordered sets $\Gamma$, which I represent as directed graphs with an edge going from $a$ to $b$ if $a \leq b$ in $\Gamma$. For example the following graph, ...
2
votes
1answer
55 views

Creating pairs of non-intersecting set from a given set

Let's say I have a set {a,b,c,d} and I want to create a list of pairs {{a,b,c,d},{}},{{a,b,c},{d}},{{a,b,c},{}},... such that there is no intersection between each pair, and they do not need to use ...
2
votes
1answer
61 views

If I have numbered elements, I there a simple way to put them in a list? [duplicate]

I've defined manually 32 elements as w1, w2, w3,..., w32....
2
votes
1answer
58 views

Calculate plausibility in Dempster-Shafer theory

I want to use Mathematica to show which subsets of a power set are required to calculate the plausibility for a given set in a power set. This has lead me to compute a summation with a ...
2
votes
0answers
72 views

Is there a way to make a set of all real numbers within a range? [closed]

Is there a way to create a set of all real numbers within a range? For example, the range between 1300 and 1500, including 1500 in normal distribution. Thank you very much. My problem exactly: $A$ – ...