Questions tagged [combinatorics]

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

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Using UnrankPermutation with Maximize

I want to try and use Maximize with UnrankPermutation to find Costas Arrays (or as close as possible) for a given length l with first two elements l, 1. A permutation array that maximizes the number ...
Eriek's user avatar
  • 817
0 votes
2 answers
77 views

How to make a function that outputs a mesh region object or some other geometric object that represents a cake number?

The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that ...
Peter Burbery's user avatar
8 votes
2 answers
484 views

Drawing Delannoy paths

I want to take the code for a Wolfram Demonstration for a Delannoy number and make a function that can return a list of Delannoy plots. The code is available from the download link. The demonstration ...
Peter Burbery's user avatar
9 votes
1 answer
352 views

Can you give a faster implementation with Mathematica for these q-analog functions?

Now(2023), Mathematica has some QFunctions for q-anlaog. See Official Documentation. e.g.: QPochhammer QFactorial ...
138 Aspen's user avatar
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1 vote
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How to generate a list of Langfor pairings?

I am wondering how to make a function that makes a list of Langford pairings named LangfordPairings that takes an integer n as output and if Langford pairings exist for that number, they output the ...
Peter Burbery's user avatar
3 votes
1 answer
101 views

How to make a function that returns all super distinct partitions?

I am working on distinct partitions. I recently created a function StrictIntegerPartitions. This is from the book Integer Partitions by George E. Andrews at Pennsylvania State University and Kimmo ...
Peter Burbery's user avatar
8 votes
4 answers
686 views

Design a function that gives all strict partitions of an integer

A strict partition of an integer has all distinct parts. There are no duplicates like 1 in {5,3,1,1} for 10. All the parts are unique. Sylvester created a bijection between the partitions of an ...
Peter Burbery's user avatar
4 votes
3 answers
169 views

Generating all complete pair-wise listing of a starting list

It might well turn out that this question has already been asked; my problem is that I don't know how to describe it succinctly enough to search. I have a list of 12 elements. If I take 2 elements ...
CrimsonDark's user avatar
1 vote
0 answers
37 views

Sequence reconstruction from ordered subsamples

Given a sequence (we'll assume of integers) like seq = {1, 0, 0, 1, 2, 0, 1} I can take a random permutation ...
b3m2a1's user avatar
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1 answer
121 views

How to calculate the number of partial derangements of a multiset in Mathematica?

I have found some helpful information on enumerating derangements at https://math.stackexchange.com/questions/4645664/the-number-of-partial-derangements-of-a-52-card-deck-ignoring-suits, https://sites....
Peter Burbery's user avatar
1 vote
1 answer
120 views

Fixing code for a combinatorics problem

The problem I am solving is: Determine all possible values of positive integer $n$, such that there are $n$ different $3$-element subsets $A_1,A_2,...,A_n$ of the set $\{1,2,...,n\}$, with $|A_i \cap ...
matrix42's user avatar
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1 vote
1 answer
251 views

Enumeration of a sequence involving closure operators

Let us call a collection $\mathcal{F} \subseteq \mathcal{P}(X)$ special if it satisfies the following two conditions: $\emptyset, X \in \mathcal{F}$ For all $U, V \in \mathcal{F}$, it holds that $U \...
user227351's user avatar
7 votes
2 answers
526 views

How can I correctly use LazySubsets from Wolfram's Lazy package?

I know that Subsets[list] gives the power set of list and Subsets[list,{k}] gives all subsets containing exactly $k$ elements. ...
licheng's user avatar
  • 1,851
2 votes
1 answer
172 views

Finding induced subgraphs that are also trees

Given a graph $G$ with $n$ vertices, I need to find a subgraph consisting of $m$ vertices $\{v_1,\ldots,v_m\}$, and the induced subgraph of this subgraph should also be a tree. For example, suppose $G$...
Dotman's user avatar
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1 vote
1 answer
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Additive graphs code

For $n\geq 1$ the fibonacci sum graph on the set $[n]=\{1,2,\ldots,n\}$ denoted by $G_n$, is the graph with vertex set $[n]$ and edge set $\{uv, u+v=F_i, \text{for some}\quad i\}$. I wrote the ...
d.y's user avatar
  • 143
2 votes
0 answers
105 views

Is FindShortestTour really exact? [closed]

I have read online that the FindShortestTour function on Mathematica uses the Concorde TSP solver, which is meant to provide exact solutions. However, I have been playing with this problem on my own, ...
slithy_tove's user avatar
4 votes
2 answers
191 views

How to find a Hamiltonian walk of a graph?

Edit: After John L.'s reminder, there is a specific term, namely "Hamiltonian walk" for my previous question. See How can we find a shortest closed walk passing through all vertices?. So I ...
licheng's user avatar
  • 1,851
4 votes
4 answers
264 views

Efficient generation of n-bit base-m Gray code with adjacent bit changes

How can I generate n-bit base-m Gray code in Mathematica, where only 1 bit changes at a time and all possibilities are covered? I have been hitting my head against a metaphorical wall for a few hours ...
More Senne's user avatar
5 votes
3 answers
242 views

Plot diagonal lattice path

I'd like to plot lattice paths like RUURUD where R is a step to the right, U is a step above ...
sankiago's user avatar
1 vote
1 answer
97 views

Arrange 1-n^2 in n×n grid satisfy products of rows equal to products columns

For which $n\in\mathbb{N}$ is it possible to arrange $\{1,…,n^2\}$ in an $n\times n$ grid so that the set of products of columns equals the set of products of rows? I can find solution for $3\times 3$ ...
expression's user avatar
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4 votes
0 answers
66 views

Can FindMinimumCostFlow be trusted?

So, I recently began to use graphs algorithms in Mathematica notebooks to solve an unbalanced assignment problem. After running the algorithm, I wanted to check that the total flow was equal to the ...
WaterFox's user avatar
  • 185
1 vote
2 answers
123 views

Delete the subsets containing the same $2$ integers present in other subsets

From my previous question, if I consider a list like this: $\{$$\{$$\{$$1,2,3$$\}$,$\{$$4,5,6$$\}$$\}$, $\{$$\{$$1,2,4$$\}$,$\{$$3,5,6$$\}$$\}$, $\{$$\{$$1,2,5$$\}$,$\{$$3,4,6$$\}$$\}$, $\{$$\{$$1,2,6$...
user967210's user avatar
5 votes
3 answers
284 views

Distribute arguments over a function in all ordered combinations

I'm looking for a function that can do this ...
Albercoc's user avatar
  • 946
4 votes
1 answer
158 views

How to generate 3-subsets that satisfy certain conditions without post-filtering?

Edits: In fact it is a set partition problem. I have a set as follows: ...
licheng's user avatar
  • 1,851
7 votes
3 answers
237 views

Permutations with subsets not containing the same elements

I would like to define a function of two integer variables $ \{n, k\} $, with $ k | n $, that would print all the possible permutations of the first $ n$ positive integers, such that the subsets of $ ...
user967210's user avatar
2 votes
1 answer
98 views

Find all ways to split a list into k sublists (of different length)

I would like to write an efficient code for splitting a set into k disjoint subsets, whose union would be the input set. The input set is represented by sorted lists with no repetitions, and the ...
wedelfach's user avatar
6 votes
1 answer
165 views

Issues with FindPlanarColoring

I tried to use FindPlanarColoring on the following planar graph: ...
A. Kato's user avatar
  • 351
3 votes
1 answer
82 views

Generating all $k$ combinations from $n$ objects [closed]

Suppose I have $n$ numbers $\{1,2,\cdots,n\}$, is there a very quick way of generating $k$-combinations using Mathematica?
Apocalypse's user avatar
0 votes
1 answer
95 views

Counting number of (non distinct) integer partitions into k

I want to count and generate the number of non distinct integer partitions into k. I know that IntegerPartitions[n,{k}] returns the partitions of integer n into k. E.g. IntegerPartitions[4, {2}] ...
00123456's user avatar
0 votes
0 answers
45 views

Arranging 4 identical items in 7 spots [closed]

There are 4 unique items, for the sake of the example call them balls. Each ball is exactly the same, and we need to see how many different ways those 4 balls can fit in those 7 slots. I am not sure ...
Jack G's user avatar
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3 votes
1 answer
260 views

Enumeration of a certain sequence III

Let’s call a collection $\mathcal{F} \subseteq \mathcal{P}(X)$ satisfying: $\emptyset, X \in \mathcal{F}$ For all $U, V \in \mathcal{F}$ it holds that $U \cap V \in \mathcal{F}$. special. We can ...
user227351's user avatar
4 votes
2 answers
195 views

Mathematica can't find Minimum sum under integer constrains

I'm trying to verify a solution to a simple probability problem using Mathematica. Here's the problem: A drawer contains red socks and black socks. When two socks are drawn at random, the probability ...
mikemykhaylov's user avatar
3 votes
4 answers
304 views

Verifying a combination problem using subsets

The question is shown below. The handwritten answer is one of the methods of the mark scheme. This method "seemed" ok, but we are not so convinced about the Total of 140 ways. Also, there is ...
CasperYC's user avatar
  • 1,460
4 votes
3 answers
237 views

How to solve combination problem with mathematica?

How to find the smallest n s.t: $$\binom{2500-n}{50}/\binom{2500}{50} < 0.5$$
omg's user avatar
  • 163
1 vote
1 answer
79 views

Enumerating unlabeled phylogenetic trees

The following code comes from OEIS A000311 which is labeled phylogenetic trees. The function mtot enumerates the labeled trees. ...
Daniel Geisler's user avatar
4 votes
0 answers
112 views

Finding a large clique of an impractically large generalised Kneser graph

My original problem statement is simple. Find a maximal clique of $k$-length subsets of of a set of $n$ items, clique members sharing at most $s$ items with any other. This is the maximal clique of a ...
kirma's user avatar
  • 18.6k
5 votes
1 answer
413 views

Enumeration of a certain sequence I

Lets denote by $a(n)$ the number of families $\mathcal{F} \subseteq \mathcal{P}(X)$ on a finite set $X$ with $n$ elements satisfying: $\emptyset, X \in \mathcal{F}$ For all $U, V \in \mathcal{F}$ it ...
user227351's user avatar
2 votes
1 answer
151 views

Enumeration of a certain sequence II

Denote by $a(n)$ the number of families $\mathcal{F} \subseteq \mathcal{P}(X)$ on a finite set $X$ with $n$ elements satisfying: $\emptyset, X \in \mathcal{F}$ For all $U, V \in \mathcal{F}$ it holds ...
user227351's user avatar
3 votes
3 answers
350 views

How to get all possible sums or possiblity of sum three numbers?

Got motivation from this and I'm trying to do this: {#1 , #2 , #3, #1 + #2 + #3} Where #1, #2, #3 are integer numbers from 1 to ...
hana's user avatar
  • 2,678
1 vote
2 answers
198 views

Generating Lyndon words modulo mirroring operation and substituion

I have two letters A,B. I want to generate all words say up to length 22 with the following properties. There is no "canonical" list so any such list will suffice, though there are many ...
2132123's user avatar
  • 647
-2 votes
1 answer
92 views

Could a function such as Slot be used in this genetic code analysis? [closed]

...
Youvan's user avatar
  • 583
0 votes
1 answer
109 views

Create list with integer partitions satisfying some conditions

I want to create a function PartSet[N_,M_] of two positive integer variables which outputs a list of all pairs of integer partitions for all integers up to $M$ ...
Benighted's user avatar
  • 1,317
1 vote
1 answer
61 views

Sorted Tuples without Filtering

Say I have a list $L$ where the elements can be sorted into some canonical order. I want to use Tuples[L,m] but I only want the output lists to be sorted and ...
Ken Robbins's user avatar
2 votes
2 answers
402 views

Using the generalised binomial theorem to expand an expression

I would like to use Mathematica to compute the following expansion: $(1+x)^\rho= 1 + \rho x +\dots$ for some $|\rho|<1$ as for example explained here. I tried the Series expansion functions ...
Hirek's user avatar
  • 483
2 votes
1 answer
67 views

Choosing numbers whose divisors can be partitioned into subsets having the equal sum

How can we find the list of natural numbers between 100 to 10000, whose positive divisors can be partitioned into three subsets such that sum of all the elements in three subsets will be equal?
Anirban Roy's user avatar
5 votes
1 answer
63 views

Picking integer compositions with certain descent patterns

I am trying to find a nice way to pick out all the integer compositions (ordered partitions) of an integer $n$ that satisfy a given pattern of descents between some adjacent elements. Writing a ...
Brian Hopkins's user avatar
7 votes
1 answer
440 views

Tuples optimization challenge

Consider a function that for a given integer $0\le n <256$ computes the number of leading zeros in its binary representation. ...
yarchik's user avatar
  • 17.5k
4 votes
1 answer
199 views

Choosing a subset of a set based on the sum of its elements

How can we choose a subset of a set based on the sum of the elements of the subset? For instance, n=6 dn=Divisors[n] sn=DivisorSum[n,#&] Is it possible to ...
Puneeth's user avatar
  • 41
6 votes
1 answer
235 views

Combine each element with all the others in sublists

Suppose that I have a list of numbers list = {{{1, 0}, {-1, 1}, {0, -1}}, {{-1, 0, 1}, {-1, 1, -1}, {-1, -1, 0}, {1, 1, 0}, {1, -1, 1}, {1, 0, -1}}} I would like ...
Alessandro Mininno's user avatar
0 votes
1 answer
110 views

Deleting sublists based on a criterion

I generated a list as follows ...
Jin Siang's user avatar

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