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

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2
votes
1answer
90 views

Mathematica doesn't know about the absorption identity? [closed]

The well-known binomial absorption identity states that $$n\binom{n-1}{k-1} = k \binom{n}{k}$$ However, Mathematica gives ...
5
votes
3answers
121 views

How to partition a set with a condition on subsets?

I want to partition a set of $n$ elements into $k$ subsets with a condition For example: partitioning this set {1,...,5} into 3 subsets with this condition: if $|i-j|<d$ then $i$ can't be with $j$ ...
0
votes
0answers
60 views

Enumerating all orientations of an undirected graph

Given an undirected graph $G$, an orientation of $G$ is a directed graph obtained by assigning every edge a direction, a superorientation of $G$ is a directed graph obtained by orienting every edge in ...
1
vote
1answer
61 views

grouping binary vectors into minimal number of sets

I have a set of binary vectors that I would like to group into a minimal number of sets. A set can be formed when it contains all combinations of elements that vary within that set. Example: for ...
1
vote
1answer
58 views

Fast way to compute intersection of equivalence classes

There is a set $S=\{1, 2, \dots, m\}$ and $n$ equivalence relations on the set: $a \sim_i b $, where $a,b \in S$, $i=1, \dots, n$. Now we define $a \sim b$ iff $ a \sim_i b$ $\forall i=1, \dots, n$. ...
4
votes
1answer
86 views

Closed form probability random walk will hit k >=1 times in n steps

I'm using Mathematica to try to solve http://quant.stackexchange.com/questions/24970 and came across what seems like a simple question: if you take a standard random walk of ...
8
votes
4answers
850 views

Tuples with one “joker” digit?

I'd like to create an array of all possible length 11 combinations of 1, 2, and the number 3, BUT with the number 3 only appearing zero or once in each combination. I tried: ...
10
votes
4answers
328 views

Efficient way to make subsets of list with placeholders

I have an arbitrary list of unique elements: lst = {a, b, c, d} Documentation allows finding subsets with same number of elements, say ...
6
votes
1answer
194 views

How to efficiently find all combinations of the letters in an alphabet given a condition

Problem: I want to find all unique expressions with n number of terms that contain all the digits (or characters) in alphabet. ...
3
votes
1answer
132 views

Efficiently generating tuples with Outer

I'm trying to efficiently generate tuples of lists of objects that satisfy a given criterion. The similar questions that I have found on this website end up finding a specific workaround for the given ...
1
vote
1answer
45 views

Construct all possible sets of pairs [duplicate]

I am looking for a nice way of constructing all possible pairings of a given list. Currently I am using the brute force approach of sieving the 2-partitions of all permutations. ...
4
votes
2answers
111 views

How can I make this code to count Hamiltonian paths faster?

I have this very basic code to count Hamiltonian paths in a graph: ...
15
votes
3answers
477 views

Generating Tuples with restrictions

I am interested in a certain subset of all tuples. Generating all with Tuples and then filtering is wasteful, and will "blow up" very quickly. For a concrete ...
4
votes
2answers
106 views

`IntegerPartitions` without duplicates

I need to apply a function to integer partitions of many integers, but only the partitions without duplicate numbers. Select[IntegerPartitions[n], DuplicateFreeQ] ...
1
vote
1answer
30 views

No of integral solutions with restrictions [closed]

x+y+z+w=n,where x<=w,y<=w. total number of non negative integral solutions of this equation?is there any closed form formula. what is the generalized formula across any number of variables?
1
vote
0answers
61 views

Finding correct combination of functions

I am trying to write code where I have an array $S$ or numbers in any order [5,4,2,1,....] Then I have a specific set of functions that I can write. ...
6
votes
5answers
143 views

Simple Enumeration of Coin Tosses

How do I enumerate a sample space with up to 6 coin tosses where 4 Heads ensures a win. For e.g {HHHH},{HTHHH},{TTHHHH},{HTTHHH} etc.I tried the following but I do not know how to do a variable length ...
5
votes
2answers
148 views

How to make pairs of Young diagrams appear?

I have the following Young diagrams {{{0}, {2}}, {{0}, {1, 1}}, {{1}, {1}}, {{2}, {0}}, {{1, 1}, {0}}} where you can interpret each pair as following: For ...
1
vote
1answer
72 views

Combinatorica and DualPartition function (for a Young diagram)

I am trying to understand how to evaluate the arm and leg functions of a Young tableaux using Mathematica. To do so I need the Combinatorica package. Then apparently the command ...
5
votes
1answer
103 views

Finding the reduced permutations of six numbers

I am trying to use Mathematica to find the following set of permutations: $$\sum_{\rho\in \tilde{S}_{n+2}} {\rm sgn}(\rho)\eta^{\mu_{\rho_{(1)}}\mu_{\rho_{(2)}}} $$ where $$ ...
2
votes
2answers
150 views

Refining subset relations

People who do combinatorics (like me) are often faced with the following problem: For a list of combinatorial objects (vectors, permutations graphs,etc.), we know what multi-set of values it ...
5
votes
1answer
74 views

What does the Combinatorica function: NumberOfPermutationsByType return?

I am using Mathematica 9. If I input: NumberOfPermutationsByType[{2, 2, 1, 1}] Mathematica returns 1/8. I was expecting ...
1
vote
0answers
152 views

Exceeding time constraint of 300 seconds when taking coefficients of some expressions from schur polynomial [closed]

I have written a code that takes coefficients of some expressions from schur function, but it seems to take a lot of time, and Mathematica will stop after 300 seconds saying that it's over the time ...
4
votes
1answer
199 views

Random Partitions

I want to write a function RandomPartition to partition a vector of length n into p partitions of varying (random) lengths. For example with ...
0
votes
1answer
132 views

How to get all possible combinations of this list? [closed]

I'm trying to get all possible combinations of {0,-1} for a certain length. So let's say I want length 2. Then I want my output to be ...
3
votes
1answer
119 views

Way to generate all multisets

I have a set $\left\{\{1,2\}, \{3,4\}, \{5,6\}, \{7,8\}\right\}$ (for example) and want to generate all sets of $n$ elements with repetition but without counting the same multiset twice. So I want my ...
2
votes
2answers
138 views

How to find all possible paths with as many edges between two same vertices?

Suppose I have an undirected graph G = Graph[{1 <-> 2, 2 <-> 3, 2 <-> 3, 3 <-> 4}] I used ...
8
votes
3answers
228 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 ...
5
votes
0answers
128 views

Number of 4-colorings of Johnson solids

I want to know the number of 4-colorings for all Johnson solids. This is equivalent to evaluating the flow polynomial for the corresponding polyhedral graphs at $k=4$. I tried the following to get ...
23
votes
1answer
689 views

Efficient lazy weak compositions

In Mathematica all weak k-compositions of integer n can be generated using permutations of integer partitions: ...
5
votes
0answers
168 views

Visualising a 1-(50,15,15) design

The problem I have is the visualisation of a $1-(50,15,15)$ design. That is a set of $50$ points and $50$ blocks (lines), so that each point is on $15$ lines, and each line contains $15$ points. My ...
7
votes
3answers
199 views

generating integer partitions

Mathematica can generate integer partitions of an integer $N$. For example, IntegerPartitions[4] quickly gives ...
2
votes
1answer
116 views

Need Help Writing code to find Capparelli Partitions

I am trying to add multiple criterion to IntegerPartitions[n] so that it sorts only partitions that fit the criterion. It creates a list of list of numbers in ...
17
votes
3answers
471 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 ...
0
votes
0answers
63 views

Hook Length Formula and Ferrer's Diagram

So, I am new to using Mathematica, and trying to write some code that needs to use hook length of each cell in Ferrer's diagram of a partition. I first thought of using for loops to manually count ...
0
votes
0answers
39 views

How to get partial results from Subsets[]? [duplicate]

Oftentimes I am searching for the first item in a sequence that satisfies some property. For example, consider the subsets of prime numbers whose total is prime. To start generate them, we could ...
10
votes
5answers
491 views

Find all the possible ways of partitioning a list into a set of pairs of element

I have a list {x1,...,xN} where N is even, and I need to find all the possible ways to split it into pairs of elements, e.g. the ...
5
votes
3answers
87 views

Conditional subset generation

I am trying to accomplish the following task: Given a list of coordinates of n points in the plane, I need to find subsets of all points that share the same ...
0
votes
2answers
87 views

Generating polynomials with conditions on coefficients

I want to define polynomials with coefficients given in some range. Namely, let $p$ be a prime number and $n$ be a positive integer. For all positive integer $k\leq n$ I want to generate all ...
8
votes
1answer
343 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 ...
5
votes
2answers
125 views

How expand Binomial[n, k] for k >= 6? [closed]

Binomial[n, k] is converted to a polynomial only for k less than 6. ...
6
votes
1answer
361 views

Efficiently find all connected subgraphs

Is there a way to generate all the connected subgraphs of a graph in mathematica without going through all the subsets of the nodes and checking if the subgraph is connected (which will be ...
6
votes
1answer
321 views

Find exponential generating function from the first few terms

The function FindGeneratingFunction computes the ordinary generating function of a sequence, given a sufficient number of initial terms. I have two questions in ...
3
votes
3answers
212 views

Permutations on elements a>b && b>c

A={1, 2, 3, 4, 5} Permutations[A, {3}] I need to print all permutations where the first number is bigger than the second and the second number is bigger than the ...
2
votes
3answers
105 views

Permutations and recurrence equation

First problem: I need to show all Permutations with length 4 of this elements {x, y, z, w, t} but with this condition: the element z mustn't be after element t. I ...
1
vote
1answer
54 views

series combinations

is there any possibility of displaying all possible series of the form: "1+/-2^2+/-3^2+/-...+/-n^2", where one can choose the sign before the each term and knows the numbers of the terms in the ...
6
votes
2answers
196 views

Subsets or Outer?

How do I generate all possible subsets of a list of positive numbers (with at least 1 of them), given that each of these positive numbers subvariates itself on its input value and its multiplicative ...
5
votes
2answers
156 views

Combinatorics: Placed errors

Consider a vector of length n where each element can take one of the values U, X, ...
2
votes
2answers
85 views

Arrangements (?) from permutations of rows in a triangle, is there a simpler way to program this?

I am generally confused about integer valued polynomials, and how to count them. Trying to learn the subject I started by listing permutations of the rows in a lower triangular table: $$\displaystyle ...
1
vote
1answer
108 views

Computational Complexity of HypergeometricPFQ

What is the computational complexity of HypergeometricPFQ? I got a result of a product of a multinomial and HypergeometricPFQ and I was wondering if that would be considered a closed form solution ...