Questions on the use of Mathematica in combinatorics, including the Combinatorica add-on package.
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 ...
19
votes
2answers
735 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 ...
16
votes
3answers
388 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 ...
16
votes
7answers
785 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 ...
15
votes
4answers
423 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 ...
14
votes
6answers
828 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:
...
14
votes
5answers
490 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
...
14
votes
1answer
275 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?
13
votes
3answers
334 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 ...
11
votes
7answers
1k 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 :
...
11
votes
5answers
698 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 ...
11
votes
2answers
327 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
264 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 ...
9
votes
4answers
426 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 ...
9
votes
3answers
244 views
Permutations[Range[12]] produces an error instead of a list
This input:
Permutations[Range[12]]
Results in this (error) output:
...
