# Questions tagged [combinatorics]

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

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### Getting dataset whose cumulants match user-provided values?

I'm interested in getting list of numbers whose cumulants match user-specified list of values. Below is an example that works for list of length 2, but I'm interested in generalizing it to higher ...
0answers
35 views

### Symbolic Subset Sum Problem

I am interested in solving the following problem with Mathematica, but I do not know if it can be done or how it could be done. Given a finite set of terms $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
1answer
74 views

### NextKSizePartition, or how to partition a set into subsets of size $k$ but incrementally

This question might seem very much like the linked one below but it differs in a very special way; Mr.Wizard suggested I start a new post: Partition a set into subsets of size $k$ What I want is to ...
2answers
105 views

### Combinations with specific total

From the values: ...
2answers
131 views

### Stars and Bars representation

How can I visualise/represent "Stars and Bars" in Mathematica? Say I have $n$ balls and $k$ slots to fill (or not to fill) with balls, e.g. when $n=4$ and $k=4$, ...
4answers
212 views

### Finding all the lines that can be defined a set of points

Input ten Points, calculate every possible straight line from each possible pair of points and check if any of the other points are on the lines. Is something like this possible in mathematica? and ...
1answer
62 views

### Tuples with more criteria

I have seen that there is question here which does almost what I wanted to ask but it's not quite what I wanted. Efficiently generating tuples with Outer What I would like to have is a Tuples of a ...
5answers
379 views

### A replacement for NextPermutation in Combinatorica [duplicate]

Does anyone know of a replacement for NextPermutation in Combinatorica? The problem with loading Combinatorica is that it interferes with new functionality which I ...
1answer
112 views

### Generating an efficient way to compute einsum?

Given an einsum like below, how could I generate an efficient computation graph for it? $$X_{ik} M_{ij}M_{kl} X_{jl}$$ The indices range from $1$ to $d$ and the goal is to minimize computation time ...
1answer
67 views

### Generating summation formulas for factorized 4th moments

I'm interested in getting summation formulas for the following expression, in Einstein summation notation, with indices ranging from $1$ to $d$ $$c=X_{ik}M_{ijkl}X_{jl}$$ Here $M_{ijkl}$ is ...
2answers
219 views

### Generating set partition diagrams

I recently came across a very nice illustration of set partitions on wikipedia (Partition of a set article) I need to reproduce this diagram in order to modify some things, does anyone have a good ...
2answers
68 views

### Permutations of $\{1, 2, \dots, n\}$ [duplicate]

When I try Permutations[Range[1, 12]]; // AbsoluteTiming I get {53.6949, Null} and with ...
1answer
65 views

### Coloring ladder rung graphs

I can use various algorithms to list all proper $k$-colorings of the vertices of the ladder rung graph $nP_2$, the first six are show below. Is there a quick way in Mathematica to list all proper $k$-...
2answers
96 views

### Counting k-colorings of a graph

Combinatorica can list all $k$-colorings of the vertices of a graph $g$, which is a coloring of the vertices with no two colors adjacent, and using no more than $k$-colors: ...
1answer
57 views

### Counting the number of strings starting with “t” and containing 2 vowels and 2 consonants

I generated a list of strings that match the criteria in the title as follows: ...
1answer
89 views

### Recursive solution to the extended Josephus problem [duplicate]

The Josephus Problem is described here, with extension of killing every $k$th problem. In the simple case where every other person is killed, we can also use the binary trick. ...
2answers
79 views

### Finding Non-Simple Paths of a Given Length on a Graph

For the following graph: ...
2answers
297 views

### How to extract coefficients of a generating function like this one, using a computer?

For example if we have the generating function $G (x) = (1 + x + ... + x^k)^{10}$ and we want to calculate the coefficient of $x^{3k}$ as a function of $k$: What is the best way to go about it using ...
4answers
219 views

### Maximum of determinant of $n\times n$-matrix with elements 0 and 1

Generalizing https://math.stackexchange.com/questions/3265627/largest-value-of-a-third-order-determinant-whose-elements-are-0-or-1 I'd like to propose two related problems (a) find the maximum value ...
1answer
115 views

### Non-flat partitions of a set

A non-flat partition of a set is one where, when the elements of the set are on a grid, the partition does not contain subsets with elements from the same row. When the set is more irregular the same ...
1answer
65 views

### Question about FindKClique

Say we have a graph: g = CompleteGraph[5]; and that we want to find all the triangles in g. I tried to use ...
1answer
62 views

### Generating integer partitions with fixed first element

I'm trying to generate all integer partitions where the first entry is a fixed number i.e. all young diagrams with first row/column fixed. I'm aware of the function IntegerPartitions[n] and I could ...
0answers
33 views

### Triangulations of a convex polygon

I have a piece of code which finds all triangulations of a convex polygon. It is known that a number of such triangulations for a given $n$-gon is is given by ($n-2$)th Catalan Number, so for instance,...
0answers
56 views

### Four color theorem in Mathematica [closed]

The four color theorem is a theorem about graphs (as in graphs and networks) and it was proved with the aid of a computer. To date, there is no hand-checkable proof. The software that was used to ...
1answer
92 views

### How to generate all the combinations with repetition?

I have $K$ variables. Each variable can take any value form a set with $N$ elements. We have $N^K$ possible solutions (permutations with repetition, when at each time slot we can choose among $N$ ...
2answers
303 views

### How to generate all the combinations? [duplicate]

There are $N$ optimization variables, $v_1,v_2,\cdots,v_N$. and $v_n\in{0,1,2,3,\cdots,K}$. Let $N=10$ and $K=5$. How can I generate all the possible combinations? For example, the first ...
1answer
52 views

### How make create all possible lists of twelve elements? [closed]

How can I create all possible lists of twelve elements when each element can be -1 or 1. That is, 2^12 different lists.
1answer
39 views

### Expanding integer compositions

Quick version: I would like Mathematica code that, for instance, turns {3,1,2} into {3,3,3,1,2,2}. More formally, given positive integers $c_1, \ldots, c_t$ which sum to $n$, produce the length $n$ ...
1answer
39 views

### Reverse the reccurence mirrorwise

Let be a recurrence for polynomials $R_{m,j}$ ...
1answer
34 views

### Different result with HypergeometricPFQ

I have a following sequence: Table[Sum[Sum[(1 + j + k + n)!/((1 + j + k) j! k! ), {j, 0, n}], {k, 0, n}], {n, 1, 5}] (* {16, 542, 31488, 2646024, 292224000} *) ...
1answer
533 views

5answers
701 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. ...
0answers
37 views