Questions on the use of Mathematica in combinatorics, including the Combinatorica add-on package.
0
votes
0answers
34 views
How could I find the correct values for every array that would lead me to unique summation number for every unique chain? [migrated]
I have 9 arrays, each array has 9 values, I need to get the proper values in every value's position for every array, and that would give my a completely unique summations for every value's chain from ...
0
votes
0answers
34 views
Generating partitions of a set with a specified size of the parts [duplicate]
I tried the following (inspired by the answer here)
myList = {a, b, c};
Needs["Combinatorica`"];
SetPartitions[myList]
and I got this answer,
...
1
vote
1answer
55 views
How to enumerate multisets
Given the eight-element set {1,2,3,4,5,6,7,8}, I would like to enumerate all multisets (subsets with repetition) of size n, where n >=3. For example, with n = 3, the sets {1,1,1}, {1,1,2}, ..., ...
0
votes
0answers
45 views
Generating partitions of a set [duplicate]
Is it possible to get Mathematica to generate all possible partitions of a set of objects?
(..or equivalently if it can be made to do the cumulant expansion or at least the Gaussian special case of ...
5
votes
1answer
74 views
How do I expand StirlingS2[n, 10] in terms of elementary functions?
I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
4
votes
1answer
118 views
Combinations which do not have elements in common
I can choose 2 letters from the four letters $\{A,B,C,D\}$ in 6 combinations using the combination formula
$$\frac{n!}{ r! (n-r)!}$$
...
3
votes
1answer
69 views
Looking for a package regarding Schur Polynomials and Kostka numbers
I'm currently looking for any Mathematica package that involves Schur polynomials and/or Kostka numbers.
More generally, I'd be happy with anything that expands on symmetric polynomials in general. ...
2
votes
2answers
177 views
How to determine all cases consistent with constraints
Suppose that $(i, j), (k, l)$ and $(m, n)$ are pairs of non-negative integers, satisfying the following constraints:
$$i < j,\;\; k < l, \;\; m < n$$
and
$$ (i, j) < (k, l) < (m, ...
2
votes
1answer
86 views
How can I prevent these warnings while using ParallelTable
I have this code to find all the permutations of a set of letters that form legal words.
...
6
votes
3answers
160 views
Counting the number of a specific type of permutation
In the theory of cumulants of vector-valued random variables, the following types of formulas appear:
\begin{equation}
\theta^i \theta^{jk} [3] = \theta^i \theta^{jk} + \theta^j \theta^{ik} + \theta^k ...
7
votes
2answers
140 views
Solving variant of the knapsack/money-changing problem
I'm trying to solve a variant of the knapsack/changing money problem where I have a set of a few numbers and I'm trying to find the linear (integer) combinations of them which are close to a given ...
6
votes
2answers
136 views
Find all permutations with a condition
How can I find all the permutations of {a, b, c} where a + b + c = n?
For instance: if ...
3
votes
2answers
122 views
What function returns all possible permutations with repeating list elements? [closed]
Let's say I want to find a sample space of such experiment:
There are three exits from the box: Left (L), right (R) and front (F). Three mice have been put in that box. Find the sample space of an ...
4
votes
2answers
133 views
Partition a set into $k$ non-empty subsets
The Stirling number of the second kind is the number of ways to partition a set of $n$ objects into $k$ non-empty subsets. In Mathematica, this is implemented as ...
2
votes
1answer
89 views
How to evaluate the sum over a hyperplane
I have difficulties in evaluating the following expression:
$$\sum_{\small n_1+...+n_{k}=m-k}\; \prod_{i=1}^{k}\frac{1}{(n_i+1)(n_i+2)}$$
I have tried the function ...
1
vote
1answer
89 views
Finding integer partitions one at a time
I am writing a small program and I need to calculate integer partitions of a handful of numbers. In my code I just run IntegerPartitions[k,{n}] and then iterate through the results. Since I only use ...
3
votes
3answers
132 views
Need Help Writing (a Pascal) Matrix in Mathematica
I want to write a function $f[n]$ in Mathematica which gives me an $n\times n$ lower triangular Pascal matrix with a row of zeros in between each nonzero row. That is, I want the matrices
...
4
votes
2answers
301 views
Exact cover solution
Is it possible to get a exact cover solution(s) and/or number of possible solutions in Mathematica?
14
votes
6answers
852 views
Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
Looks like a question for pupils, right?
In fact if the available math symbol is limited to $+$, $-$, $\times$, $/$ then it's easy to solve:
...
2
votes
0answers
196 views
Generating a function which outputs possible chemical reactions
I want to make a list of chemical reactions and I write them down in a $\require{mhchem}\LaTeX$ format. They are of the following form
$$NA_n^i+MB_m^j \rightarrow \hat NA_{\hat n}^{\hat i}+\hat ...
2
votes
3answers
227 views
How to find all graph isomorphisms in FindGraphIsomorphism
I found the second definition of the function FindGraphIsomorphism not working.
Here's the definition Mathematica 8 gives:
...
14
votes
5answers
506 views
Get number of combinations without “forbidden patterns”
I need to get the number of all combinations of binary digits in an 8-digit binary number, but minus some "forbidden" patterns like:
xxxx0xx1
x1xxx0xx
x1xxx0x0
...
20
votes
2answers
736 views
Plotting an Unreasonable Function
Without getting into too much detail, the following (very complicated) function recently appeared as a solution to a combinatorics problem I've been thinking about:
$$P(n) = \frac{52!}{52^{52}} \cdot ...
4
votes
1answer
278 views
(Efficiently) Generating graphs with vertex degree 3 for all vertices
I'm working on a graph theory problem, and given $n$ vertices, I would like to be able to generate all non-isomorphic connected graphs (not necessarily simple) with $n$ vertices, each having degree 3. ...
3
votes
0answers
161 views
Find all permutations with reversals / cyclic permutations removed
I have a list of all non-cyclic permutations of n labels. How can I get rid of all elements which are redundant in the sense that they are the inverse of another one. For instance if n=4, the ...
6
votes
4answers
236 views
permutation as product of transpositions
How can the permutation that takes{-f, -i, i, -e} into {-e, -i, i, -f} be realised as a sequence of nearest neighbour ...
3
votes
1answer
186 views
3
votes
2answers
174 views
Combinatorica: Girth[] and FindCycle[] disagreement
Warning: run the following code in a fresh Mma session, as some symbols could be shadowed (depending on your Mma version)
While trying to answer this question, I fell into the following:
...
23
votes
4answers
855 views
What is the fastest way to count square-free words?
Background
A word is a string of letters in an alphabet. A square-free word has no adjacent repeating substring. For example, (in the ternary alphabet of {0,1,2}) the words 00, 012121, and 0212012021 ...
6
votes
3answers
505 views
Find cycles of graphs with both directed and undirected edges
I need to enumerate all the simple cycles of a graph which has both directed and undirected edges, where we can treat the undirected edges as doubly directed. (Specifically, I am looking at the Cayley ...
11
votes
2answers
335 views
Word Squares and Beyond
A word square is a set of words which, when placed in a grid, read the same horizontally and vertically. For example, the following is an English word square of order 5:
...
10
votes
3answers
267 views
Generating Linear Extensions of a Partial Order
Given a set $S$ and a partial order $\prec$ over $S$, I'm looking for a way to "efficiently" generate a list of linear extensions of $\prec$. Suppose the partial order is given by a ...
6
votes
2answers
420 views
Finding all partitions of a set
I'm looking for straightforward way to find all the partitions of a set.
IntegerPartitions seems to provide a useful start. But then things get a bit complicated.
...
3
votes
0answers
69 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
...
3
votes
1answer
374 views
How to create tournament bracket
I'd like to create a tournament bracket using Mathematica. I've looked around online, but haven't found any examples yet. Can someone show me how to do this? Specifically, I'd like to have a ...
21
votes
4answers
2k views
Looking for “Longest Common Substring” solution
I'm looking for robust code to solve the "Longest Common Substring" problem. I can just code it up from that description, but I'd thought I'd ask here, first, in case someone knows of an ...
13
votes
3answers
338 views
Determining all possible traversals of a tree
I have a list:
B={423, {{53, {39, 65, 423}}, {66, {67, 81, 423}}, {424, {25, 40, 423}}}};
This list can be visualized as a tree using ...
18
votes
3answers
452 views
How to load a package without naming conflicts?
This question applies to any package, but I encountered this problem while working with graphs.
There are symbols in the Combinatorica package (such as ...
4
votes
1answer
375 views
Is it possible to generate a Hasse Diagram for a defined relation?
I'm looking for a way to create a Hasse Diagram from a given partial order binary relation.
The relation will be given explicitly, for example: ...
14
votes
1answer
281 views
When to use built-in Graph/GraphPlot vs. Combinatorica
What are the pros and cons of using built-in Graph/GraphPlot (and related) types vs. types in the Combinatorica package?
3
votes
1answer
173 views
Combinatorica Graph from Edge List
Can someone provide an example of a Combinatorica-based graph which uses ShowGraph and Graph and takes in an explicitly defined list of edges (not some auto-generated graph). I have not been able to ...
7
votes
1answer
196 views
Mathematica function/package for shuffle permutations
Does anyone knows a way to compute a list of all (p,q)-shuffles in mathematica?
For a definition of the shuffle permutations see for example http://ncatlab.org/nlab/show/shuffle
I'm dreaming of a ...
6
votes
1answer
202 views
Finding all length-n words on an alphabet that have a specified number of each letter
For example, I might want to generate all length n=6 words on the alphabet {A, B, C} that have one ...
9
votes
2answers
148 views
NumberOfSpanningTrees command not working correctly
I am attempting to use the Combinatorica NumberOfSpanningTrees command for all n-cycle graphs from 3 to 30. I am trying to get a ...
15
votes
4answers
433 views
How do I generate the upper triangular indices from a list?
I have some list
{1,2,3}.
How do I generate nested pairs such that I get
{{1,2},{1,3},{2,3}}?
That is I'd like a way to ...
11
votes
5answers
728 views
Partition a set into subsets of size $k$
Given a set $\{a_1,a_2,\dots,a_{lk}\}$ and a positive integer $l$, how can I find all the partitions which includes subsets of size $l$ in Mathematica? For instance, given ...
9
votes
4answers
445 views
Efficiently Visualising Very Large Data Sets (without running out of memory)
I have put a few really hard problems in combinatorics up against Mathematica 8. I'd have to say that it works really well, until you want to view the data. If you look at my question Advanced ...
8
votes
3answers
587 views
Advanced Tupling
I had asked this question before but I guess I did not make the question clear enough and I apologize for that. Here is the problem: Tuples gives me more data than ...
7
votes
1answer
481 views
How to apply a permutation to a symmetric square matrix?
Given a symmetric square matrix, how can I apply a permutation to the rows and columns (i.e. the same permutation to both the rows and the columns) such a way that the new structure of the matrix ...
16
votes
7answers
812 views
How to Derive Tuples Without Replacement
Given a couple of lists like a={1,2,3,4,6} and b={2,3,4,6,9} I can use the built-in Mathematica symbol ...
