Questions tagged [combinatorics]
Questions on the use of Mathematica in combinatorics, including the Combinatorica add-on package.
31
questions with no upvoted or accepted answers
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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 ...
- 415
5
votes
0
answers
219
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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 ...
- 51
4
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0
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70
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Can FindMinimumCostFlow be trusted?
So, I recently began to use graphs algorithms in Mathematica notebooks to solve an unbalanced assignment problem.
After running the algorithm, I wanted to check that the total flow was equal to the ...
- 185
4
votes
0
answers
113
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Finding a large clique of an impractically large generalised Kneser graph
My original problem statement is simple. Find a maximal clique of $k$-length subsets of of a set of $n$ items, clique members sharing at most $s$ items with any other.
This is the maximal clique of a ...
- 18.7k
4
votes
0
answers
111
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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.) ...
- 153
4
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0
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107
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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
...
user1489762
3
votes
0
answers
102
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/...
- 151
3
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0
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158
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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 ...
- 291
3
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0
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89
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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 ...
- 337
2
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0
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112
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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:
...
- 21
2
votes
0
answers
91
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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 ...
- 427
2
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0
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454
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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 ...
- 963
2
votes
0
answers
675
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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_{\...
- 1,485
1
vote
0
answers
91
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How to generate a list of Langfor pairings?
I am wondering how to make a function that makes a list of Langford pairings named LangfordPairings that takes an integer n as output and if Langford pairings exist for that number, they output the ...
- 1,663
1
vote
0
answers
38
views
Sequence reconstruction from ordered subsamples
Given a sequence (we'll assume of integers) like
seq = {1, 0, 0, 1, 2, 0, 1}
I can take a random permutation
...
- 46.6k
1
vote
0
answers
52
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Enumerating labeled graphs on n vertices
I'm trying to enumerate the labeled graphs on $n$ vertices having at most $e$ edges. I thought GraphData /@ GraphData[n] and then filtering by edge count would do ...
- 21
1
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0
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79
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Triangulation of Point Configuration
I was going through the documentation of Mathematica but couldn't find any built-in function that can find all possible triangulations for a given set of points.
For example, if I have the following ...
- 1,122
1
vote
0
answers
61
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.
...
- 2,449
1
vote
0
answers
101
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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:
...
1
vote
0
answers
147
views
Is there a way to predict permutations that consist of sets?
SequencePredict is a function that predicts the next value from the arranged data.
But I want to use the data for the combination to predict the next combination(...
- 1,460
1
vote
0
answers
42
views
Permute using symmetric vs alternating groups
Why does this happen?
Permute[{0, 0, 0}, SymmetricGroup[3]]
(* {{0, 0, 0}} *)
Permute[{0, 0, 0}, AlternatingGroup[3]]
(* {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} *)
- 11
1
vote
0
answers
62
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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:
...
- 63
1
vote
0
answers
91
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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. ...
- 31
0
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0
answers
42
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Convex hull aborts kernels (reproducible)
11.0.0 for Microsoft Windows (64-bit) (July 28, 2016)
ReleaseID -> "11.0.0.0 (5570737, 2016072801)
a set of 32 points :
...
- 1,333
0
votes
0
answers
52
views
Building and Plotting a discrete CDF
I'm trying to plot the CDF of a simple "nCr" experiment:
A box contains 4 screws and 6 nails. Two items are drawn at random without replacement. Let X be the number of nails drawn.
I built a ...
- 101
0
votes
0
answers
46
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 ...
- 46.6k
0
votes
0
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135
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 $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
- 101
0
votes
0
answers
55
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,...
- 1,294
0
votes
0
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104
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Combinatorica and MultiplicationTable in Mathematica 11
I try to use
<<Combinatorica`
or call
IntervalSlider; Needs["Combinatorica`"]
or call
...
- 903
0
votes
0
answers
92
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
...
- 1,326
0
votes
0
answers
172
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Tuples with restrictions
SHORT VERSION
Given 2t Ranges, each of length len, what is the fastest way of finding the ...
- 6,755