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Questions tagged [combinatorics]

Questions on the use of Mathematica in combinatorics, including the Combinatorica add-on package.

3
votes
1answer
41 views

Using FindInstance for Identifying Feasible Planar Solutions in a 3D Latin Hypercube

Consider a $3d$ lattice latin hypercube with $n$ steps in each dimension, so it has $n^3$ positions. Coordinates $X, Y, Z \in \{1,2,...n\}$. I want to find all of the permutations of them where they ...
1
vote
3answers
106 views

Handling cases of cross terms for multi-sums

I have expressions consisting of many multi-sums and I would like to extract cross terms out of them. Consider a simple example: $$ \sum_{m_1=1}^M \sum_{m_2=1}^M \sum_{m_3=1}^M \sum_{m_4=1}^M (x_{m_1}...
4
votes
5answers
676 views

Sum of list numbers smaller than one goal

I have five values ​​that I would like to add them so that they can be equal to or less than 3000. ...
1
vote
0answers
37 views

Binomial coefficients for negative entries [duplicate]

Mathematica evaluates the binomial coefficient $\binom{-1}{-1}$ to 1. That agrees with an application I have in mind. However many books, such as Concrete Mathematics, e.g. see here, define $\binom{...
5
votes
3answers
412 views

Find position without iterating

The code below solves for the four value of $m_i$ for a given pair of $(N_m,M_m)$. where $$ m_1+m_2+m_3+m_4 = M_m\\ |m_1|+|m_2|+|m_3|+|m_4| = N_m $$ Edit 2 New Sorting I have now realised that the ...
0
votes
1answer
35 views

How can I construct binomial terms using the Binomial function? [closed]

I want to construct a table of the terms Binomial[n, i] t^i (1-t)^(n-i) where i goes from 0 to ...
1
vote
1answer
38 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
79 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
32 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
58 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
324 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
28 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
49 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
261 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
74 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
43 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
77 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
242 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
38 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
199 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
62 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
92 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
362 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
170 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
37 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
208 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
30 views

Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica` or call IntervalSlider; Needs["Combinatorica`"] or call ...
5
votes
3answers
298 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
36 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
131 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
47 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
164 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
108 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
117 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
47 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
115 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
171 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
88 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
52 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
38 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
730 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
79 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
114 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
32 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
141 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
73 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
53 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
104 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
183 views

Generating invertible matrix with lines within a given set

Consider the set options given as below ...