# Questions tagged [combinatorics]

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

25 questions with no upvoted or accepted answers
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157 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 ...
216 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 ...
105 views

### BipartiteMatching hangs with floating-point weights in Mathematica 7 (package Combinatorica)

I am trying to use Combinatorica's BipartiteMatching algorithm on a weighted graph. I need to use real numbers as weights. If I try the following ...
99 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/...
127 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 ...
84 views

### Generating All Regular Multigraphs -- Issue with Solve and/or FindInstance

I'm looking to generate all regular multi-graphs over $n$ vertexes and of degree $d$ in mathematica (side note: $n,d$ are fairly small, this problem gets unmanagable very fast). So here $n,d$ are my ...
95 views

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90 views

### Why Does Subsets[...,{n}] not Output a Packed List, Even Though it Doesn't Unpack?

Assume list is packed. I expect Subsets[] is a structural operation because it depends on the number of elements, not on what ...
112 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: ...
88 views

### The number of real values assumed by combinations of complex roots of a decic

Define complex conjugate as the pair of complex numbers $a+bi,a-bi$. Assume you have 5 such pairs and they are the 10 roots $x_i$ of a 10th-deg equation with integer coefficients. In general, how many ...
432 views

### Get path to end nodes in directed (partially cyclic) graph

I have a large directed graph containing small loops. I would like to extract all paths to all end nodes (no VertexOutComponent) with a given path length $n$. I ...
648 views

### Generating a function which outputs possible chemical reactions

I want to make a list of chemical reactions and I write them down in a $\require{mhchem}\LaTeX$ format. They are of the following form NA_n^i+MB_m^j \rightarrow \hat NA_{\hat n}^{\hat i}+\hat MA_{\...
60 views

### Matroids in Mathematica?

I can't seem to find a "standard" way to implement/manipulate matroids in Mathematica. (They do not seem to be included in Combinatorica, for instance, and googling has turned up nothing.) ...
33 views

### Custom Table, for iterating over permutations

It is common that I iterate over all permutations of 1,2...,n, either by making a table or performing a sum. Instead of creating the set of all permutations, it would be better to iterate over them. ...
83 views

### How to find maximal determinant of a 5×5 or 6×6 matrix using the integers 1 to $n^2$ quickly

This code can only solve the 3 * 3 matrix: ...
41 views

### Permute using symmetric vs alternating groups

Why does this happen? Permute[{0, 0, 0}, SymmetricGroup] (* {{0, 0, 0}} *) Permute[{0, 0, 0}, AlternatingGroup] (* {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} *)
59 views

### Alternative Methods of Using Cumulative Density Functions To Obtain Probabilities

I have a CDF that is generated from the subtraction of two arrays as part of a minimization procedure. A consequence is that events in the simulation can cause the subtracted total to be less than 0: ...
84 views

### Finding correct combination of functions

I am trying to write code where I have an array $S$ or numbers in any order [5,4,2,1,....] Then I have a specific set of functions that I can write. ...
41 views

### Climbing/Descending the Multidimensional Integer Ladder

This is basically a follow-up to Climbing/Descending the Integer Ladder, but in multiple dimensions. It's basically just an index counting problem, but combinatoric blow-up makes it interesting. In ...
106 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 $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
44 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,...
63 views

### Combinatorica and MultiplicationTable in Mathematica 11

I try to use <<Combinatorica or call IntervalSlider; Needs["Combinatorica"] or call ...
86 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 ...