# Questions tagged [combinatorics]

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

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64 views

### Randomsample without repetition

I'm looking for a simple way to generate random samples of lists of integers such that each time I sample I'm sure it chooses a new random sample. This is closely related to Picking random items out ...
67 views

### Compute all trees on a given label set

Given a set of labels {a_1,...,a_n} (with some labels possibly appearing multiple times) I would like to efficiently compute all trees with n leaves labelled {a_1,...,a_n} and 2n-2 nodes. This is ...
36 views

### Climbing/Descending the Multidimensional Integer Ladder

This is basically a follow-up to Climbing/Descending the Integer Ladder, but in multiple dimensions. It's basically just an index counting problem, but combinatoric blow-up makes it interesting. In ...
67 views

### Overlay Graph3D with Graphics, with aligned coordinates

I have a Graph3D object representing a 3D lattice path ...
333 views

### How to perform a reduced knapsack problem

I have a problem statement that seems to be a reduced version of the knapsack problem, but I don't know how do it in Mathematica. The problem is as follows: Given a set, S, of integers (e.g {a,b,c,...}...
69 views

### using DeleteCases with CoprimeQ

first let me show what I have working correctly f = Permutations[Range, {3}] Riffle[f, Apply[CoprimeQ, f, {1}]] now I would like to automate the deletion of a ...
485 views

A fun combinatoric puzzle that's popped up in my work that I think would be cute to have a Mathematica solution to, if anyone wants to give it a go. It's basically a ladder climbing/descending problem ...
39 views

### Number of partitions of an integer with a fixed number of parts

Is there an easy way in Mathematica to find the number of partitions of $n$ into $k$ parts? Or equivalently, the number of partitions of $n$ with largest part equal to $k$? I realize the function ...
79 views

### Solving 190 equations from a list of 2x20 elements [closed]

I have a list of 20 pairs of elements, say {{x1, y1}, {x2, y2}, ...}, and I want to solve the following equation for a constant c...
113 views

### Visualizing set partition lattice

There's a cool visualization of set of all partition over 4 elements ordered by refinement, which makes it a lattice. Can Mathematica be used to generate these kinds of visualizations automatically? ...
81 views

### From a bag of n balls, with c colours, and d draws count how many variations are possible? [closed]

First, the objective is not to use formulas for combinations, or permutations. The objective is to use loops(for, while, etc.) to make Mathematica count the number of possible variations/sequences of ...
196 views

### Generating all symmetric binary matrices of order up to 7?

I want to create all symmetric binary matrix with order up to 7. Can anybody help in creating this? I want to obtain the subset of all symmetric matrices, with all diagonal entries being zero.
236 views

### Solving a rotating combination lock puzzle

The following puzzle appears in The House of da Vinci II and I thought it might be interesting to tackle in Mathematica: There are numbers marked on four rotating cylinders. These numbers must add up ...
62 views

### Counting terms in recursive operation

Suppose $X$ is an algebra and $T :X\to X$ is linear function. Let $L:X\to X$ be a function satisfying the following property $$L(a \cdot b)= T(a)\cdot b + a \cdot T(b)+b\cdot T(a)+T(b)\cdot a\tag{*}$$...
151 views

### Non crossing set partitions

A set partition is noncrossing if whenever four elements $a<b<c<d$ are such that $a,c$ are in the same block and $b,d$ are in the same block then $a,b,c,d$ are all in the same block. Can I ...
71 views

### How to program combinatorics problems about randomly moving cards from $A$ to $B$ to $C$ to $A$?

I have a lot of problems with the following scenario, for example, Given 3 boxes $A$, $B$ and $C$. The box $A$ contains 2 identical cards $x$, 4 identical cards $y$ and 1 card $z$. The box $B$ ...
91 views

### How to find formula from a table?

I recently started using mathematica for simple tasks like simplifying etc. First of all let me say if this breaks any rules I apologize since I'm a novice in using this and I'll remove the question. ...
367 views

### How to remove any words containing two adjacent characters with different in both cases and letters?

I have a list of permutations of ABCabc and I want to remove any permutations with two adjacent characters with different in both cases (uppercase and lowercase) ...
229 views

### List of tuples without duplicates & repeated values [duplicate]

Given some number nand set of values vals, I want to obtain all the tuples/permutations of size ...
132 views

### How to check whether a string contains a certain number of consonants and vowels?

I am trying to check the answer of the following problem programmatically. A manual calculation by hand must be possible but it is not my question. Given a string ...
324 views

### Lozenge tilings

I am trying to produce these lozenge tilings as a way of encoding plane partitions. I need to produce something like: but am using demonstration code like this: ...
83 views

### How to find the closed loop number of an array [closed]

I want to find the minimum number of swaps required to reset an array. This problem has many applications in linear algebra. The key point of this question is to find the number of closed loops in ...
226 views

### How to express permutation as the least number of exchanges

If there are grammatical or terminological errors in the following description, please help correct: In some problems, it is necessary to find out what minimum number of exchanges can change a list ...
86 views

### Why Does Subsets[…,{n}] not Output a Packed List, Even Though it Doesn't Unpack?

Assume list is packed. I expect Subsets[] is a structural operation because it depends on the number of elements, not on what ...
81 views

### Finding the best-fitting subsets by frequencies of list item groupings

Suppose I have a list of groups: {{1,2,3,4}, {1,2}, {3,4}} In this example, 1 most commonly appears within a group that contains ...
53 views

### How to list all possible 3-tuples with entries of the 3 tuples from 2 different sets?

If there are two sets $A={1,2,3,4}$ and $B={5,6,7,8}$, how to construct list of all possible 3 tuples where the first two entries are any element from set $A$ and the 3rd entry is any element from set ...
### $q$-multinomial series
I have the following code, which produces a $q$-multinomial coefficient, but selected randomly according to a Poisson distribution. Consider a 3D lattice path selected uniformly at random from a ...