# Questions tagged [combinatorics]

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

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152 views

### Number of 4-colorings of Johnson solids

I want to know the number of 4-colorings for all Johnson solids. This is equivalent to evaluating the flow polynomial for the corresponding polyhedral graphs at $k=4$. I tried the following to get ...
975 views

### Efficient lazy weak compositions

In Mathematica all weak k-compositions of integer n can be generated using permutations of integer partitions: ...
214 views

### Visualising a 1-(50,15,15) design

The problem I have is the visualisation of a $1-(50,15,15)$ design. That is a set of $50$ points and $50$ blocks (lines), so that each point is on $15$ lines, and each line contains $15$ points. My ...
612 views

### generating integer partitions

Mathematica can generate integer partitions of an integer $N$. For example, IntegerPartitions[4] quickly gives ...
130 views

### Need Help Writing code to find Capparelli Partitions

I am trying to add multiple criterion to IntegerPartitions[n] so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in ...
564 views

### Improving speed of code computing number of nonrepeating partitions

I need to answer the following for a number of parameters: How many ways can the integer $k$ be written as a sum of $n$ different integers ranging from $1$ to $m$? My initial attempt was the ...
49 views

### How to get partial results from Subsets[]? [duplicate]

Oftentimes I am searching for the first item in a sequence that satisfies some property. For example, consider the subsets of prime numbers whose total is prime. To start generate them, we could ...
2k views

### Find all the possible ways of partitioning a list into a set of pairs of element

I have a list {x1,...,xN} where N is even, and I need to find all the possible ways to split it into pairs of elements, e.g. the ...
104 views

### Conditional subset generation

I am trying to accomplish the following task: Given a list of coordinates of n points in the plane, I need to find subsets of all points that share the same x-...
154 views

### Generating polynomials with conditions on coefficients

I want to define polynomials with coefficients given in some range. Namely, let $p$ be a prime number and $n$ be a positive integer. For all positive integer $k\leq n$ I want to generate all ...
864 views

### Alternative to Subsets to generate k-combinations

I need to generare a huge number of k-combinations for a quite big set of numbers (more than 100), so I would avoid Subsets because it requires too much memory (it generates all subsets at once). I ...
332 views

### How expand Binomial[n, k] for k >= 6? [closed]

Binomial[n, k] is converted to a polynomial only for k less than 6. ...
1k views

### Efficiently find all connected subgraphs

Is there a way to generate all the connected subgraphs of a graph in mathematica without going through all the subsets of the nodes and checking if the subgraph is connected (which will be O(2^N)*O(...
142 views

### Descending order of Permutations using Select[Tuples[{5, 4, 3, 2, 1}, {3}], OrderedQ]

I was wondering if there is a possible way to still use OrderedQ and get a descending order of permutations: This is Ascending order: ...
487 views

### Find exponential generating function from the first few terms

The function FindGeneratingFunction computes the ordinary generating function of a sequence, given a sufficient number of initial terms. I have two questions in ...
255 views

### Permutations on elements a>b && b>c

A={1, 2, 3, 4, 5} Permutations[A, {3}] I need to print all permutations where the first number is bigger than the second and the second number is bigger than the ...
125 views

### Permutations and recurrence equation

First problem: I need to show all Permutations with length 4 of this elements {x, y, z, w, t} but with this condition: the element z mustn't be after element t. I ...
83 views

### series combinations

is there any possibility of displaying all possible series of the form: "1+/-2^2+/-3^2+/-...+/-n^2", where one can choose the sign before the each term and knows the numbers of the terms in the series?...
241 views

### Subsets or Outer?

How do I generate all possible subsets of a list of positive numbers (with at least 1 of them), given that each of these positive numbers subvariates itself on its input value and its multiplicative ...
180 views

### Combinatorics: Placed errors

Consider a vector of length n where each element can take one of the values U, X, ...
101 views

### Arrangements (?) from permutations of rows in a triangle, is there a simpler way to program this?

I am generally confused about integer valued polynomials, and how to count them. Trying to learn the subject I started by listing permutations of the rows in a lower triangular table: \displaystyle ...
177 views

### Computational Complexity of HypergeometricPFQ

What is the computational complexity of HypergeometricPFQ? I got a result of a product of a multinomial and HypergeometricPFQ and I was wondering if that would be considered a closed form solution ...
206 views

### Integer partitions and dice result probabilities

This is a Project Euler question, so no spoilers :] I was going to try to solve it by first finding how many ways a certain sum can be acquired from a number of dice using ...
76 views

### Create a list of all functions given a set of arguments

I'm trying to examine some patterns on the permutation of elements in finite element functions. I'd like to create a list of all functions (256 of them) on ...
913 views

### What is the fastest way to get the nth distinct permutation of a list?

What is the fastest way to write a function nthPermutation[xs_List, n_Integer] which is equivalent to Permutations[xs][[n]] but ...
250 views

### Checking if one partition is a subpartition of another

Say I've got two partitions of a list (not necessarily containing numbers, and not necessarily distinct), and I want to check that one is a subpartition of the other. Let's look at some examples: <...
191 views

### Is there a way to split a list (or number) into a specific number of parts?

I know there's a way to split a list into parts of a specific length, and I know there's a way to get all possible partitions of an integer. But I was wondering if there's a way to partition a list ...
285 views

### How to check whether elements of a list meet a condition without generating the whole list first?

I have to find the number of elements satisfying a given condition from the set: Tuples[Tuples[Tuples[{0,1},n],n],m] The condition for $n=3,m=3$ is: ...
2k views

### Finding all sublists or substrings of a given list/string

Given a list or string, how do I get a list of all (contiguous) sublists/substrings? The order is not important. Example for lists: ...
471 views

### Partition a range of integers into triples

Some time ago, I was asked to look at a simple to formulate puzzle. Consider the list of numbers {1,2, ..., 33}. Try to split this list in 11 triples, such that in ...
500 views

### Partitioning with constraints on subsets

Given the following data: constraints = {{11, 2}, {11, 3}, {11, 4}, {11, 6}, {11, 9}, {1, 6}, {5, 6}, {2, 5}}; weights = {3, 7, 3, 2, 4, 2, 2, 2, 3, 2, 1}; I ...
201 views

### Finding permuations in a specific order

I would like to find the following permutations, but need an elegant way of computing it. Ideally I would like to have a variable determine the highest number in the last element and find all ...
107 views

### Is there a minor bug in Neal Alexander's TopologicalSortAll[]?

There is an amazing answer to this question: All possible topological orderings of a graph By Neal Alexander. However, as user "dark blue" (I am not this user) notes: ...
1k views

### Partition list into a given number of sub-lists

I'm having quite a hard time with the following. I would like to partition a list into a list of sub-lists, in such a way that the number n of sub-lists is fixed. ...
122 views

### Efficient subsetting and averaging

The following code aims to average 4 groups of the values vector. Which elements belong to each group is determined by the indic ...
195 views

### Can I generate matrices with a constraint?

Say I want a way to generate matrices with the following properties, All non-diagonal elements are either $0,1,-1$ The diagonals are either $k$ or $k+1$ for some $k \in \mathbb{Z}^+$ for some $k$ ...
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 ...
603 views

### Defining Associated Stirling Numbers of the Second Kind

First, I'm new to Mathematica. I spent my undergraduate programming with Maple, and my computer crashed and I lost it. Fortunately, my university offers free Mathematica downloads to students, so ...
90 views

### Getting FerrersDiagram to work

I am trying to generate FerrersDiagram (see http://reference.wolfram.com/language/Combinatorica/ref/FerrersDiagram.html), any clues to getting it to work? I get error message for the following: ...
511 views

### Constructing a list of Cartesian coordinates of the Icosahedron

I’m learning Mathematica and I need the coordinates of the Icosahedron vertices. This is my attempt at writing a program for it. The vertex coordinates are simply all cyclic permutations and sign-...
869 views

### Enumerating all connected graphs with 9 vertices

The version of my Mathematica is 10. I generate a connected graph with 9 vertices, but find that it is not included in Mathematica. ...
450 views

### Using Permutations to create numbers

I'm a high school math teacher working on a simple high school math problem involving permutations. I like to try to check answers to some of these problems since it helps "convince" the students ...
446 views

### How to define even permutations correctly?

I define even permutations as following, but there may be some error. I use it in two different way and get different output. ...
498 views

205 views

### The algorithm of ListGraphs[n,m]

I'm not sure if this is a Mathematica problem, math problem or a CS problem, so if this is off-topic please transfer it. In the package Combinatorica there is a ...
512 views

### Making a flag with six vertical stripes

A flag is to be made with six vertical stripes by using colours yellow, blue, green and red in such a way that no two adjacent stripes should have the same colour. In how many ways is this possible? ...