Questions tagged [combinatorics]
Questions on the use of Mathematica in combinatorics, including the Combinatorica add-on package.
0
votes
0answers
14 views
how can I construct binomial terms using the binomial function?
Basically, what I want to achieve is that for variable t and 1-t so the constructed terms are the Binomial(n,i),t^i *(1-t)^n-i, i goes from 0 to n, and I do not want to sum them, I want all the ...
1
vote
1answer
33 views
How to find efficiently the independent vertex sets from a large adjacency matrix?
I have a binary adjacency matrix $M$ of size $72\times 72$. I would like to find all possible combinations of 18 non-adjacent nodes.
There are $^{72}C_{18}$ possible (adjacent and non-adjacenct) ...
5
votes
1answer
65 views
Generate list of tuples, modulo PermutationGroup
I have a permutation group, e.g.
g=PermutationGroup[{Cycles[{{1, 2}}]}]
but not necessarily limited to a single generating cycle.
What I want is to create a ...
0
votes
1answer
31 views
Sums of binomial expressions returns different and sometimes indeterminate expressions
A problem that I encountered multiple times when taking sums over expressions involving binomials, factorials, etc. is that Mathematica (version 11.2) returns indeterminate expressions when it should ...
0
votes
2answers
53 views
Tuples of elements from list excluding anything with repeated values
What I would like to do is the following.
For a given list of elements; say (0,1,2,3,4) I would like to obtain all possible combinations of five, but not the ones with ANY repeated values. That is I ...
7
votes
2answers
321 views
How to represent a product of cycles in matrix form?
I have a permutation a in a product of disjoint cycles form as follows
$a = {{(1,9,3,7)(2,11,6)(4,8,5,10)}}$
I want to represent it in a matrix form ...
0
votes
0answers
27 views
Enumerate all lists of $m$ non-negative integers that add to $n$ [duplicate]
Let $x_1,\dots,x_m$ be non-negative integers such that $\sum_{i=1}^m x_i=n$, where $m,n$ are given. How can I enumerate all such lists of $m$ integers that add to $n$?
Note that ...
4
votes
2answers
48 views
Groupings of the Elements of a List with at Most $k$ Elements
Given a list with $n$ elements and an integer $k$ I want to get a list with all possible groupings of these n elements in sets with at most k elements. For example, given $n=\{1,2,3,4\}$ and $k=3$ I ...
3
votes
1answer
250 views
How to calculate all possible resistances made from 5 distinct resistors in series and/or parallel? [closed]
Five distinct resistors resistors={1,2,3,4,5} are given. The objective is to find a list of all possible resistances obtained by configuring all these resistors in ...
2
votes
1answer
65 views
Find All Compositions of an Integer
I can use the Combinatorica package to produce all integer compositions of the integer $n$ into $k$ parts by writing ...
3
votes
0answers
33 views
Package like combinat
I started using Mathematica and want to do some computation involving Characters of the symmetric group. In maple, I used to use the package combinat. The link is below
https://www.maplesoft.com/...
1
vote
3answers
68 views
How to generate the lists of $0 \leq m \leq X$ integer values so these values add up to $X$
This must be basic, but my Mathematica (and overall programming) skill level is too low to find a handy solution:
I need to generate all possible lists of $m$ integers (I call these integers $x_i$'s, ...
8
votes
3answers
231 views
Find k smallest sum n-tuples
Given a collection of sorted lists {l1, l2, ...} I need to find the smallest k index tuples taken from these lists by summed ...
2
votes
1answer
37 views
Simpifying expressions with binomial coefficients
I wrote:
Simplify[Binomial[n, k] - Binomial[n - 1, k]]
I expected Mathematica to simplify this according to Pascal's identity to:
...
6
votes
2answers
195 views
All adjacency matrices of size n
What would be a concise way to get all adjacency matrices of size $n$, e.g. for $n=2$, these $(2^2)^2$ matrices:
...
3
votes
1answer
58 views
Selecting special tuples from a big list, and dealing with memory limitations
OK, I'm working on some music theory stuff since that's my hobby. This is what I want to do:
...
4
votes
1answer
81 views
Testing for Symmetry and Regularity in (Graph-Theoretic) Graphs
I know my way around Mathematica pretty well, however I have not been able to find any built-in functionality for testing a (graph-theoretic) graph for being
symmetric (arc transitive) – this is the ...
12
votes
4answers
348 views
How to generate all involutive permutations?
Take a finite set $S$ (i.e., a list). An involutive permutation is one that squares to the identity. How can we generate all such permutations efficiently, that is, without generating all permutations ...
5
votes
2answers
167 views
Pattern for k distinct elements of a set of n elements
I would like a pattern which takes as an argument a set with $n$ elements, and an integer $k$ which is less than $n$ and greater than 1, and which matches against any $k$ distinct elements of the set, ...
1
vote
0answers
33 views
Generating list of binomial outcomes [closed]
As an example, imagine if I have a set of 3 coins and I want to generate a list of possible coin states. I know I can brutishly execute:
...
4
votes
2answers
183 views
Scramble matrix under some condition
Assume I have a matrix.
(mat = Partition[Range@9, 3]) // MatrixForm
mat$=\left(
\begin{array}{ccc}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & ...
0
votes
0answers
28 views
Combinatorica and MultiplicationTable in Mathematica 11
I try to use
<<Combinatorica`
or call
IntervalSlider; Needs["Combinatorica`"]
or call
...
5
votes
3answers
297 views
Implement the partition function
I am trying to write my own version of the PartitionsP function. Here is my code:
...
13
votes
1answer
1k views
How to generate all Feynman diagrams with Mathematica?
I'm using the words "Feynman diagrams" for indexing purposes, but the question is in fact purely graph-theoretic.
Given a list n={n1,n2,...} of non-negative ...
0
votes
1answer
33 views
Separate list elements into groups of two in all possible ways? [duplicate]
Consider a list with an even number of elements, e.g.
list = {1,2,3,4};
I would like to have a function fun that produces all ...
5
votes
2answers
116 views
Find independent tensor products using Young Tableaux
I'll present a very simplified version of what I really need to do.
I have the following 2-rank tensors $h_{\mu\nu}$ , $\xi_{\rho\sigma}$, $k_{\alpha\beta}$ where $h$ and $k$ are symmetric under ...
0
votes
1answer
46 views
A problem of a sequence and its sum
{a(n)} is such a sequence, satisfying,
For all a(i) ∈ {a(n)}, a(i) =1 or -1
Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0.
For a given n , how many {a(n)} are there?
0
votes
1answer
162 views
Easy number theory problem
$p$ is an odd prime number，$S = \{x \mid 1 \leq x \leq 2p, x \in \mathbb{Z} \}$,
$A$ is a subset of $S$, satisfying
$\operatorname{card}(A) = p$
$\sum\limits_{x\in A} x \equiv 0 \pmod p$...
4
votes
4answers
101 views
Obtain all the (multinomial) subsets
I have a set, lets say: set = {1, 2, 3, 4, 5}
I want to get all the possible subsets with 1, 2, and 2 elements.
What I did was to generate all possible ...
4
votes
3answers
114 views
A sudoku-like collection puzzle
I have a puzzle. I'm given a collection of $n$ lists, all of equal (but arbitrary) length $l$. These lists are made up of 0s and a few filled in numbers, like so:
{ {0, 2}, {0,0}, {6, 0}, {0,0} }
...
1
vote
1answer
45 views
Permute a list of elements given a pattern
I have this function f and a pattern
pattern = f[h[x]]f[h[y]]
where h is a generic ...
4
votes
1answer
104 views
Subsets of a multiset
The function Subsets[] returns the subsets of a finite set of elements. This function has a shortcoming in that it treats repeated elements distinctively. Is there ...
4
votes
1answer
162 views
solid partitions generator
According to Wikipedia, a solid partition of $n$ is a three-dimensional array $n_{i,j,k}$ of non-negative integers (with indices $i,j,k \geq 1$) such that $$\sum_{i,j,k} n_{i,j,k}=n$$ and $$n_{i+1,j,k}...
0
votes
1answer
86 views
Probability of empty urns for undistinguishable balls in distinguishable urns
Distinguishable balls in distinguishable urns is a well known problem in probability theory and can be easily simulated through Montecarlo simulations. Here we provide our code for n balls and m urns:
...
0
votes
1answer
49 views
function that generates a list of all plane partitions of a given dimension
Is there a function in Mathematica that generates a list of all plane partitions of a certain dimension $n$? This paper describes the algorithm, but I still find it a bit tricky to do it myself.
0
votes
1answer
36 views
Configuration integral for a variable number of points on a torus
If I have $n$ points on the surface of a torus, and want to check the Euclidean length of all "three-hop paths" between two (newly added) fixed points $s,t$ at distance $||s-t||$ apart, I need to ...
5
votes
3answers
654 views
Combine two lists with all possible combinations
I have the following lists:
list1={1,2,3,4,5};
list2={10,20,30,40,50};
I want to combine these lists such that each element in ...
2
votes
1answer
76 views
Testing if a Graph is Balanced
The "average degree" of a graph $G = (V,E)$ is $$\frac{2|E|}{|V|}$$ or simply $2l/k$, i.e. twice the number of edges divided by the number of vertices.
With $H$ a graph, if we simply write $d(H)=2l/k$...
2
votes
2answers
110 views
Counting the permuted partitions
With IntegerPartitions[7], I have partitions of 7 into integers that are smaller than 6 as follows.
...
2
votes
0answers
31 views
Apply all possible permutations into a function [duplicate]
I need to create a function that returns all possible trebles of integers that sum up to a given number. For example, is n=2 then I need something like this:
...
1
vote
1answer
120 views
Creating subsets of lists of lists which have certain properties
PREFACE:
This question is about a proper algorithm and its implementation. I will explain the problem as detailed as possible and will give my current algorithm as well as two more possible solutions ...
1
vote
2answers
72 views
Can this expression be written in a simpler form?
Observe the following Wolfram Mathematica code which results in a table of integers:
...
2
votes
1answer
51 views
Unified class of an object type “Group”?
Does Mathematica support an unified class for "group-type" objects? Or, less general, for groups with a fixed defined representation in Mathematica?
For example:
...
1
vote
0answers
100 views
Partition a set of n objects into k subsets? [duplicate]
Is there some function recently added to Mathematica that facilitates forming all partitions of a n-element set into k subsets?
In other words, something that easily gives the same thing as what <...
3
votes
2answers
179 views
Generating invertible matrix with lines within a given set
Consider the set options given as below
...
2
votes
2answers
217 views
Cartesian product of more than two sets
Here you see how to produce a cartesian product of two sets. How can we obtain the cartesian product of three or more sets? CartesianProduct[l1,l2,l3] doesn't work....
3
votes
2answers
82 views
Obtaining all possible ways to concatenate matrices
With Prepend we can add a line to all matrices in a set, like this:
...
2
votes
0answers
89 views
Combinatorial Optimization of NFL Games
This is a "fun" optimization problem that was prompted by an NFL betting pool. Each week you pick one team to win. If that team wins you stay in the game. If it loses you're out. The catch is that ...
2
votes
1answer
80 views
Sorting of permutations
I would like to output the list of possible permutations of 4 indices but sorted in a certain way. I know that I can the list of possible permutations with
...
3
votes
0answers
59 views
Lazy tuples made from arbitrary lists [duplicate]
I am dealing with Tuples of n lists each having potentially different length:
longList = Tuples[list1, list2, ..., listn]:
Since I have to iterate over the ...
