# Questions tagged [combinatorics]

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

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### 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 ...
3k 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 ...
2k 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 ...
2k views

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

This input: Permutations[Range[12]] Results in this (error) output: ...
987 views

### Lazy lists of Tuples and Subsets

I'm trying to build a lazy list that evaluates the n'th m-tuple or subset of a given list using Mathematicas ordering without calculating all the Tuples. The purpose is to allow for example the ...
4k 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. ...
1k 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 ...
3k 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 ...
509 views

### Lazy form of Tuples/Outer to loop over list of lists

This is less a question and more asking if someone has implemented this already, with more skill. I need to perform the Outer-like generalized outer product of a ...
718 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 n = 3...
2k 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: ...
2k views

### Shuffle product of two lists

I want to do the following: I have two lists {a_1,...a_n}, {b_1,...,b_n} and I would like to build now all shuffles out of this. This means all unions of these ...
872 views

### Alternative to Subsets to generate k-combinations

I need to generare a huge number of k-combinations for a quite big set of numbers (more than 100), so I would avoid Subsets because it requires too much memory (it generates all subsets at once). I ...
653 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 ...
2k views

### How to generate all Feynman diagrams with Mathematica?

I'm using the words "Feynman diagrams" for indexing purposes, but the question is in fact purely graph-theoretic. Given a list n={n1,n2,...} of non-negative ...
4k 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 ...
483 views

### Mathematica implementation of Zeilberger's algorithm (previously done in Maple)

I have this Mathematica code: ...
2k views

### Finding all sublists or substrings of a given list/string

Given a list or string, how do I get a list of all (contiguous) sublists/substrings? The order is not important. Example for lists: ...
183 views

### Exploring all combinations of parameters

I often need to explore a large parameter space, e.g. making dozens of plots using a range of parameters. This looks something like: ...
2k views

### Faster derangements?

I wonder what is the fastest method to generate derangements? Both the Combinatorica function and Martin Ender's answer to Permutations of lists of fixed even numbers are based on filtering the ...
978 views

### Efficient lazy weak compositions

In Mathematica all weak k-compositions of integer n can be generated using permutations of integer partitions: ...
570 views

### Improving speed of code computing number of nonrepeating partitions

I need to answer the following for a number of parameters: How many ways can the integer $k$ be written as a sum of $n$ different integers ranging from $1$ to $m$? My initial attempt was the ...
5k 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: ...
2k 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 ...
1k views

### How to correct my code for solving the Josephus problem?

Problem Description Recently, I have been reading the book Schaum's Outline of Mathematica (2nd Edition), where I encountered the problem: Flavius Josephus was a Jewish historian of the first ...
939 views

### Memory efficient generation and selection of tuples

The short of this question: I need to find a bunch of n-tuples of {0,1} which do not fail to satisfy a set of (non-linear polynomial) equations, without hogging up all of my memory by trying to ...
995 views

### How to count all cliques (not just maximal ones) in graphs?

How can I count the numbers of $r$-cliques in a graph? In other words, the number of triangles, the number of $K_4$, the number of $K_5$ etc. I have tried for example ...
1k 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: ...
3k views

### How to improve the performance of solutions to Project Euler (#39)?

This is the problem 39 of Project Euler, which I asked in the chat room two days ago. My original code runs as slowly as snails, and finally I got two answers from JM and Rojo. Unfortunately, both of ...
712 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 ...
510 views

### Partitioning with constraints on subsets

Given the following data: constraints = {{11, 2}, {11, 3}, {11, 4}, {11, 6}, {11, 9}, {1, 6}, {5, 6}, {2, 5}}; weights = {3, 7, 3, 2, 4, 2, 2, 2, 3, 2, 1}; I ...
595 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 ...
3k 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 : ...