# Questions tagged [combinatorica]

Combinatorica provided a large amount of functionality in fields such as graph theory and permutations.

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### How many graphs are there on 4 nodes with degrees 1, 1, 2, 2?

I know just the basic operations on graphs using Mathematica. But I want to know how to write a code that prints all the possible combinations of a graph with a specified number of edges. Take for ...
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### Orbits of a set $X$ under the action of cyclic permutation $T$

Let $X$ be a set defined as $$X = \{\{\sigma_1, \dots, \sigma_L\} \;|\; \sigma_i = 0,\dots ,n-1\}.$$ Furthermore, let $T:X\longrightarrow X$ be a cyclic permutation  T\cdot\{\sigma_1, \dots, \...
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### Multiple colors on a single graph edge?

Is there any way to put two colors on one single graph edge? For example, I want to highlight two cyclic paths (red and blue). But, if I put the two colorings into one image, it does not work as I ...
58 views

### How can directed graphs be constructed from a list of lists of vertex pairs in Mathematica 7 by Graph or by MakeGraph?

I let Mathematica 7 construct a list of lists of vertex pairs, e.g.: s = { {{1,2},{2,3}}, {{1,2},{1,3}} } The s of the example contains two directed graphs. How ...
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### How can I introduce vertex labels into a graph

How can I introduce vertex labels into a graph in Mathematica 7 with Combinatorica? I create graphs with Graph or GraphPlot, ...
692 views

### Counting number of inversions

Is there an inbuilt method to find the number of inversions in a set of numbers? I found Inversions in Combinatorica but when I ...
449 views

### Dijkstra without Combinatorica

There is some overlap between Combinatorica and the Graph related framework but there are also various elements missing. As far as I can see there is no 'Dijkstra' method or algorithm in Mathematica ...
63 views

### Mathematica IntervalGraph

I wanted to visualize an Interval Graph.Documentation says there exists a function IntervalGraph in Global which used to be in package Combinatorica before ...
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### Combinatorica and DualPartition function (for a Young diagram)

I am trying to understand how to evaluate the arm and leg functions of a Young tableaux using Mathematica. To do so I need the Combinatorica package. Then apparently the command ...
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### Change VertexSize in ShowGraph from Combinatorica

I am using HasseDiagram from Combinatorica (in 10.1). I am very happy to have found HasseDiagram because I am drawing Hasse ...
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### Non-trivial partitions of numbers using Combinatorica

I have made a code which gives back partitions of numbers in two Young diagrams (one Young diagram is trivial). For example, the partitions of 1 are ...
88 views

### Cycle index of a graph automorphism group

I want the cycle index of the group of automorphisms of a (say 3 X 3) grid graph. I can produce the elements of the group with: ...
182 views

### Using CombinatoricaListNecklaces in v9

I am using Mathematica for visualization of DeBruijn graphs. However, I am having a bit of trouble using ListNecklaces. I want to know how many cyclic shifts of ...
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### How to compute the automorphisms of graphs with multiple edges?

I try to compute the Automorphisms of graphs with multiple edges from its AdjacencyMatrix but failed. The following code shows ...
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### The algorithm of ListGraphs[n,m]

I'm not sure if this is a Mathematica problem, math problem or a CS problem, so if this is off-topic please transfer it. In the package Combinatorica there is a ...
988 views

### Young Tableaux Miscellanea

I have a problem which is mostly neatly described by using Young Tableaux. Mathematica seems to have these Tableaux built in, except that the Tableaux function is ...
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### What does the Combinatorica function: NumberOfPermutationsByType return?

I am using Mathematica 9. If I input: NumberOfPermutationsByType[{2, 2, 1, 1}] Mathematica returns 1/8. I was expecting <...
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### Seeking a way to generate sequential partitions of a list using built in or Combinatorica functions [duplicate]

This code generates all "sequential partitions" of a list: ...
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### PermutationReplace does not seem to work when Combinatorica is open. Is there a function that is equivalent.?

I want a permutation to act on a set. For example: I want the permutation {2,1,3,5,4} to act on the set {2,3,4} by returning {1,3,5}. I need to do this in the same code that has functions that need ...
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### How best to use or to emulate the “obsolete” Combinatorica command Contract?

The obsolete Combinatorica package has a command Contract for contracting an edge in a graph. Below is my very clunky attempt to work with up-to-date graph objects ...
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### How can I temporarily suspend the Combinatorica package?

Sometimes after I load the Combinatorica package by entering Needs["Combinatorica`"], I need to use Mathematica for something like: ...