Tagged Questions

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

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10
votes
1answer
129 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
146 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 $$\frac{n!}{ r! (n-r)!}$$ ...
5
votes
1answer
284 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. ...
3
votes
2answers
298 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
236 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
404 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
269 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
291 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 ...
4
votes
2answers
717 views

What function returns all possible permutations with repeating list elements?

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
241 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
142 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 ...
2
votes
1answer
147 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
191 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
584 views

Exact cover solution

Is it possible to get a exact cover solution(s) and/or number of possible solutions in Mathematica?
16
votes
6answers
1k 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
326 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 ...
4
votes
3answers
681 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
662 views

Getting number of binary digits combinations without “forbidden” patterns

I need to get the number of all combinations of binary digits in an 8-digit binary number, but not including those that follow some "forbidden" patterns like these: ...
21
votes
2answers
842 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 ...
5
votes
1answer
499 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. ...
6
votes
1answer
417 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
315 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
2answers
312 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
1k 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 ...
12
votes
4answers
1k views

Finding elementary cycles of (directed) graphs

I need to enumerate all the simple cycles (i.e. elementary cycles where no vertex is repeated other than the starting) of a graph which has both directed and undirected edges, where we can treat the ...
11
votes
2answers
391 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
373 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 ...
8
votes
2answers
1k 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. ...
4
votes
0answers
92 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 ...
4
votes
1answer
511 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 ...
28
votes
4answers
3k views

Looking for “Longest Common Substring” solution

I'm looking for robust code to solve the "Longest Common Substring" problem: Find the longest string (or strings) that is a substring (or are substrings) of two or more strings. I can just code it ...
14
votes
3answers
516 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 ...
22
votes
3answers
1k 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
2k 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
389 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
377 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 ...
8
votes
1answer
392 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
434 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 ...
10
votes
2answers
194 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
5answers
636 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 ...
21
votes
5answers
1k 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 ...
10
votes
4answers
715 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
2answers
859 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 ...
9
votes
1answer
826 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 ...
21
votes
7answers
1k 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 ...
8
votes
3answers
532 views

Probability problem — Rube Goldberg solution?

A user posted this question on StackOverflow which was closed as off topic: 3 people are playing a game with a standard 52 card deck. Each player is given 2 cards each, possible cards and their ...
12
votes
5answers
573 views

Permutations[Range[12]] produces an error instead of a list

This input: Permutations[Range[12]] Results in this (error) output: ...
11
votes
7answers
2k views

Combination and Permutation

How could I obtain the list of all the groups of 5 numbers taken from Range[12] such that the 2 lists have an empty intersection : ...