# 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 ...
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 ...
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 $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
105 views

### Combinations with specific total

From the values: ...
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 ...
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 ...
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 $k=4$, ...
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 ...
2k views

### Permutations[Range] produces an error instead of a list

This input: Permutations[Range] Results in this (error) output: ...
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 ...
65 views

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 $k$-...
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: ...
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 ...
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 ...
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 ...