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4
votes
1answer
72 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 ...
4
votes
1answer
199 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 ...
0
votes
0answers
43 views

how to use a tree as a key to construct a table of key values

I have an interesting problem that I was able to summarize in the form of trees, sets, and key value pairs. I have the following sets of keys and values \begin{equation} \begin{aligned} k_0 &= ...
1
vote
0answers
34 views

Solving systems of logial and set theoretic propositions

I need to allocate a couple of dozen elements into different sets, respecting some boundary conditions, and was hoping Mathematica might somehow help. A simple example: The propositions being a) a ...
2
votes
0answers
60 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: $A$ ...
11
votes
6answers
456 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: ...
3
votes
1answer
345 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 ...
31
votes
7answers
2k 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: ...
0
votes
1answer
59 views

Mining for matching elements of sets with equal divisors

This problem is extrapolated from a problem that was solved on how to manipulate lists of set outputs as a union ( Equation Autogeneration ), where the concern now is how to mine for (or attain from ...
1
vote
2answers
213 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?
10
votes
5answers
427 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 ...
16
votes
7answers
667 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 ...
11
votes
7answers
3k 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 : ...
0
votes
1answer
208 views

Inclusion-Exclusion Principle Implementation

I would like to know how I can write a Mathematica code for the Inclusion–exclusion principle. The formulas governing it are: $ P(\bigcup_{i=1}^n A_i)=\sum_{k=1}^n (-1)^{k-1} ...
0
votes
0answers
42 views

Addition of all elements of two sets with each other [duplicate]

Let $S_1=\{a_1,a_2,\ldots,a_m\}$ and $S_2=\{b_1,b_2,\ldots,b_n\}$ be two sets. I want to list all $a_i+b_j$ for each $1\leq i\leq m$ and $1\leq j\leq n$ in a set. Is there a commend in mathematica for ...
4
votes
3answers
290 views

Counting number of inversions

Is there an inbuilt method to find the number of inversions in a set of numbers? I found Inversions in Combinatorica but when I ...
10
votes
4answers
365 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 ...
2
votes
1answer
187 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 ...
11
votes
10answers
805 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 ...
3
votes
7answers
407 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 ...
11
votes
1answer
283 views

How to find longest monotonic sequence?

I have a list, for example list = {2, 1, 3, 5, 4, 6} How to find longest ascending sequence of this list? There are two meanings of this question: Find the ...
4
votes
2answers
132 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: ...
7
votes
1answer
252 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 ...
5
votes
1answer
116 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 ...
0
votes
4answers
45 views

How to multy-Set a group of lists?

I have a group of lists, for example: lists = RandomInteger[10, {100, 2}] {{6, 7}, {7, 4}, {3, 3}, ....} Now, I want to ...
14
votes
5answers
3k 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 ...
1
vote
3answers
155 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 ...
3
votes
0answers
70 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 ...
6
votes
3answers
742 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 ...
1
vote
1answer
129 views

Set theoretic operations on sets of real numbers

I have two pieces of code that produce a bunch of real numbers, say $A$ and $B$ respectively. (It is not relevant to the question, but $A$ consists of eigenvalues of the Hamiltonian of some physical ...
1
vote
2answers
2k 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 ...
13
votes
8answers
546 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, ...
10
votes
3answers
382 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 ...
4
votes
2answers
797 views

Exact cover solution

Is it possible to get a exact cover solution(s) and/or number of possible solutions in Mathematica?
2
votes
2answers
415 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 ...
10
votes
3answers
844 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 ...