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

0
votes
2answers
50 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
316 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
45 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 ...
0
votes
0answers
43 views

Randomly choose 50% of n things, but only 1% of specific k things implies what? [migrated]

Summary: If you randomly choose 50% of n entities total, but it turns out you only chose 1% of k specific pre-chosen entities, does that imply n is likely to be much larger than k? I'm trying to use ...
3
votes
1answer
242 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
54 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
32 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
67 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
217 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
31 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
193 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
56 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
68 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
329 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
32 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
163 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
26 views

Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica` or call IntervalSlider; Needs["Combinatorica`"] or call ...
5
votes
3answers
295 views

Implement the partition function

I am trying to write my own version of the PartitionsP function. Here is my code: ...
12
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
31 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
106 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
44 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
156 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
98 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
110 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
44 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
95 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
148 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
0answers
31 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
47 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
35 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
541 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
73 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
109 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
108 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
71 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
50 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
94 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
184 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
81 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
80 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
75 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 ...
0
votes
0answers
69 views

Why does a linear change of variable in a double sum enable Mathematica to obtain a symbolic answer?

I perform two equivalent sums. Mathematica returns a symbolic expression in one case but not the other. Shouldn't Mathematica be able to do either sum? First sum ...
0
votes
3answers
135 views

What does GraphData[“Cubic”, n] do?

I don't have Mathematica, yet, but I just wanted to know what the output of the following was: GraphData["Cubic", 20] I'm trying to understand how many unique not-...
0
votes
1answer
138 views

List all possible microstates and corresponding energy using mathematica.

Consider 10 identical indistinguishable particles placed on 3 energy states with energy mgh, 2mgh,3mgh respectively.List all possible microstates and corresponding energies. I am a physics student ...