# Questions tagged [combinatorica]

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

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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 $k$-...
99 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: ...
30 views

### How to find disjoint subsets such that union of the sets give the motherset or main set?

Let us define a set $\mathcal{S}=\{1,2, 3,\cdots,67\}$. I have a list of 132 subsets. I want to obtain 16(or 17) mutually exclusive subsets such that union of such 16(or 17) is equal to $\mathcal{S}$...
187 views

### How can I compute the chromatic number of a graph?

I'm starting in Wolfram Mathematica. I saw that MinimumVertexColoring [g] could be used to calculate the chromatic number of a graph, but ...
52 views

### In what order does Combinatorica's SetPartitions function list the partitions of a set?

For example, Needs["Combinatorica"] n = 4; partitions = SetPartitions[Range[n]]; Table[Print[partitions[[i]]], {i, 1, BellB[n]}] generates ...
111 views

### Find All Compositions of an Integer

I can use the Combinatorica package to produce all integer compositions of the integer $n$ into $k$ parts by writing ...
94 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/...
187 views

### Testing for Symmetry and Regularity in (Graph-Theoretic) Graphs

I know my way around Mathematica pretty well, however I have not been able to find any built-in functionality for testing a (graph-theoretic) graph for being symmetric (arc transitive) – this is the ...
47 views

### Combinatorica and MultiplicationTable in Mathematica 11

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

### Find independent tensor products using Young Tableaux

I'll present a very simplified version of what I really need to do. I have the following 2-rank tensors $h_{\mu\nu}$ , $\xi_{\rho\sigma}$, $k_{\alpha\beta}$ where $h$ and $k$ are symmetric under ...
47 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 ...
387 views

### Replacement for GraphJoin

According to MathWorld >> GraphJoin, Mathematica could compute the join of two graphs with the GraphJoin command, part of ...
83 views

### 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, ...
58 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 ...
392 views

### Combinatorica Functionality in Vers. 11.1.1

Since version 10, much of the original functionality in the Combinatorica package has been subsumed (consumed?) by new graph primitive functions. However, as per similar posts, at times there are ...
48 views

### 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 ...
78 views

### 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 ...
74 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: ...
342 views

### 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 ...
88 views

### 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 <...
179 views

### 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: ...
50 views

### 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 ...
69 views

### 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 ...
231 views

### 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 ...
188 views

### 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: ...
128 views

### Twilight Zelda Guardian Puzzle : Shortest Path Proof [closed]

I'm playing a video game right now and in it is a puzzle (see here). There are solutions to solving it (see here) on the Internet, but I'd like to know if this path is the shortest path (least amount ...
209 views

### 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 ...
173 views

### Using Combinatorica`ListNecklaces 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 ...
608 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 ...
602 views

### 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 ...
123 views

### How do I visualize the result of EdgeColoring[g]?

Combinatorica has a heuristic edge-coloring function EdgeColoring. When I execute it on a graph, the result is a list of integers. My guess is that an integer $i$ ...
799 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 ...
218 views

### Subgraph, HighlightGraph not acting as expected

I'm trying to create a simple graph from a matrix and then highlight a particular subgraph. My code (simplified from a bigger task) is as follows. I keep getting the "Subgraph::graph: A graph object ...