# Tagged Questions

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

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### 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 $k$ ...
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### 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 ...
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### defining Associated Stirling numbers of the Second Kind

First, I'm new to Mathematica. Spent my undergraduate programming with Maple and my computer crashed and I lost it. Fortunately, my university offers free Mathematica downloads to students, so here ...
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### 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 ...
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### Checking connectedness of a graph

I am trying to use the Combinatorica package in a Mathematica version 8 in the following code: ...
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### Better way to get Fisher Exact?

I want to perform a Pearson's $\chi^2$ test to analyse contingency tables; but because I have small numbers, it is recommended to perform instead what is called a Fisher's Exact Test. This requires ...
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### Permutation count for sets with multiplicities

I am able to do a permutation counr for the set {a, a, b} which gives me 3 groups. I am happy with that result. However, if the set is ...
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### Shortest polygonal path

I'd like to find the shortest distance between some points (every point must be visited), such as between these 3 points: ...
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### How can I find the derivative of a combinatorial expression? [closed]

I want to differentiate the following equation: n = (nchoosek)*p*(1 - p)^(n - k) After differentiating my result is: ...
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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 ...
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### Tools for finding minimal or almost-minimal graph vertex colorations in Mathematica v9?

I'm looking to compute minimum vertex colorations (s.t. no two vertices of the same color share an edge: http://en.wikipedia.org/wiki/Graph_coloring) for graphs in Mathematica v9 with potentially up ...
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### Equivalent Nested Loop Structure

Consider the following examples: ...
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### How to use Automorphisms[] on a graph? [duplicate]

I am having difficulty mixing the new post-Combinatorica graph data structure, with functionality apparently only in Combinatorica. I have constructed a graph using ...
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### PermuteSubgraph not working? (Combinatorica)

I am trying to write a code to perform the QAP partialling analysis (here's a paper to know more) but the part in which I "scramble" the graph with PermuteSubgraph does nothing, I am actually not ...