All Questions
Tagged with integer-partitions permutations
34
questions
1
vote
1
answer
37
views
I want to obtain partition of an integer with an initial value and
I want to obtain a partition of an Integer with an initial value and
the value following it is smaller and the value following it is smaller than the previous value and no value repeats itself.
within ...
- 31
0
votes
0
answers
28
views
Number of partitions with limited cardinality [duplicate]
We are given $k$ urns labeled from $1$ to $k$. What is the number of ways to put $n$ indistinguishable balls into the $k$ (distinct) urns, given that each urn has a limited capacity equal to $c$, ...
- 149
1
vote
2
answers
1k
views
The number 3 can be written as $3$, $2+1$, $1+2$ or $1+1+1$ in four ways. In how many ways can the number $n$ be written?
Attempt
Let $x$ be any variable
$X+0=n ; X+Y=n ; X+Y+Z=n ; \dots; X+Y+Z+A+\dots=n$ (sum of n-1 terms); $1+1+1+.......+1=n$ (sum of n terms).
So total number of ways=
$$(n-1) C (1-1)+(n-1) C (2-1)+\...
- 85
10
votes
1
answer
228
views
Unexpected result on the number of permutations with a restriction.
Let $p=(p_1,p_2,\dots,p_n)$ be a weak composition of a positive integer number $n$ into $n$ non-negative integer parts and let $k_i$ be the count of the part $i$ ($i=0,1,2,\dots$) in the composition.
...
- 26.7k
0
votes
1
answer
58
views
Combination with Restriction and Repetition
I have a number $x$, let's say $5$, and I want to sort the number out into $4$ digits so that the sum of the digits is equal to $5$, but the value of each digit cannot exceed $3$. $0$ would be an ...
- 11
0
votes
1
answer
315
views
How many ways can you add the numbers 1, 2, and 3 to create a number n?
I would like to find an equation in which, given a number n, you can find the amount of ways to add 1, 2, and 3 to create the number. The commutative rule doesn't apply; for example, 1 + 1 + 3 is a ...
user844250
0
votes
0
answers
47
views
Which of partitions of 5 correspond exclusively to even permutations?
I am ultimately want to prove that $A_{5}$ is simple and the first step in doing so is to:
$(a)$ Write out all partitions of $5.$ Which of these correspond exclusively to even permutations?
I was able ...
user777833
0
votes
0
answers
88
views
How can we map a partition of $n$ to some permutation of [1,2, ... , n]?
Here is the question I was reading:
Does every partition of n correspond to some permutation of [1,2, ... n]?
And here is a statement in the answer given there that I want to use:
If the partition is $...
user777833
0
votes
1
answer
54
views
Applying boundary conditions to counting combinatorial question [duplicate]
I was trying to count the number of natural number solutions to the equation: $x_1 + x_2 + ... + x_{11} = 20$, such that $0 \leq x_i \leq 9$, for all $i \in \{1, ..., 11\}$.
I know how to apply the ...
- 2,663
0
votes
1
answer
194
views
Integer partitions and permutations
I am given the pair $(n, \lambda)$ where $\lambda$ is a partition of $n$ such that 6 is not a part in $\lambda$. I am told to let $\lambda^*$ represent the partition of $n$ conjugate to $\lambda$. ...
- 337
0
votes
0
answers
26
views
Making a group of $p$ people with $n$ available nationalities
Making a group of p people using m out of n available nationalities can be one of these two scenarios;
$m \le p \le n$ or $m \le n \le p$.
Using p,m, and n, how to evaluate the number of ways of ...
- 5,450
1
vote
2
answers
196
views
Limit the maximum value of the composition of an integer
I was doing a coding test (already finished, so no cheating for me) and came across this problem, which I'll describe in few steps:
We have a keypad, like on cellphones, with keys from 1 to 9, where ...
- 111
0
votes
0
answers
70
views
Number of ways to partition $\{1,2,3, \dots, N\}$ into tuples where the size of no tuple exceeds $3$.
While it seems to me that the general answer is not going to be a neat formula, I really only need this for $N=4$ and $N=5$. I'm getting $61$ and $321$ respectively, but I'm not sure. Please help.
- 981
-1
votes
1
answer
89
views
Number of ordered set partitions with subset size $\leq 3$
For $n \ge 0$, let $h_n$ be the number of ways of taking $n$ (distinguishable)
rabbits, putting them into identical cages with one to three rabbits per
cage and then ordering the cages in a row. Find ...
- 434
1
vote
1
answer
951
views
Coin Combinations for any given scenario.
I am trying to work out the number of scenarios I can cover with a given set of coin combinations so I can decide when I have the optimal amount of change to carry.
For the sake of the example, lets ...
- 325
3
votes
1
answer
852
views
Counting ordered integer partition permutations of max part size
Is there a better way to do this?
The question as it was asked of me was to create an algorithm that counted the total number of ways an integer N could be partitioned into parts of size 6 or less. ...
- 31
2
votes
3
answers
1k
views
Number of ways of cutting a stick such that the longest portion is of length n
We are given a stick of length $L$ (say). We make cuts such that the longest piece is of length $n$ (say) at most.
What are the minimum number of pieces we will get and in how many ways this can be ...
0
votes
2
answers
240
views
Number of solutions using partitions for linear equation having restrictions
Here is a linear equation $$a+b+c+d=12$$ where $a,b,c,d$ are restricted to be greater than zero and less than or equal to 6.
How many set of positive integer solutions are possible using partitions ...
5
votes
1
answer
4k
views
How many permutations in S(n) have this particular type?
I'm working through the textbook A Course in Enumeration. In the section about permutations and Stirling numbers, I'm having trouble understanding problem 1.45. It is:
We fix $n \in \mathbb{N}$, and ...
- 468
1
vote
1
answer
359
views
How many partitions of $n$ are there?
Considering a partition to be an ordered $n$-tuple $(m_1, m_2, m_3, ..., m_n)$ with all the numbers $m_i$ natural, $m_1 \le m_2 \le m_3 \le ... \le m_n$, and $m_1+m_2+...+m_n=n$: how many of those $n$-...
- 851
2
votes
2
answers
171
views
How many combination of $3$ integers reach given number?
I have 3 numbers
$M=10$
$N=5$
$I=2$
Suppose I have been given number $R$ as input that is equal to $40$
so in how many ways these $3$ numbers arrange them selves to reach $40$
e.g.
$$10+10+10+...
- 23
5
votes
2
answers
360
views
How many numbers of $10$ digits that have at least $5$ different digits are there?
In principle I resolved it as if the first number could be zero, to the end eliminate those that start with zero.
The numbers that can use $4$ certain figures (for example, $1$, $2$, $3$ and $4$) are ...
- 865
0
votes
1
answer
117
views
Interpreting the table of classification of the partitions of $n$
I am going through A NON-RECURSIVE EXPRESSION FOR THE NUMBER OF IRREDUCIBLE REPRESENTATIONS OF THE SYMMETRIC GROUP $S_n$ by AMUNATEGUI. In table I, the classification of the partitions of n according ...
- 559
0
votes
2
answers
275
views
How many distinct, non-negative integer solutions are there for $2x_0+\sum_{i=1}^{m}{x_i}=n$?
We are given constants $m$ and $n$. How many non-negative integer solutions are there for $2x_0+\sum_{i=1}^{m}{x_i}=n$ satisfying the condition that$x_i\neq x_j$ if $i\neq j$?
I thought a good first ...
- 535
6
votes
3
answers
1k
views
Counting problem: generating function using partitions of odd numbers and permuting them
We have building blocks of the following lengths: $3, 5, 7, 9, 11$ and so on, including all other odd numbers other than $1$. Each length is available in two colors, red and blue. For a given number $...
- 61
0
votes
1
answer
503
views
Partition numbers with restriction on the greatest part *and* on the number of positive parts
I’m looking at partition numbers. OEIS A008284 says that the number of partitions of $n$ in which the greatest part is $k$, $1 \le k \le n$, is equal to the number of partitions of $n$ into $k$ ...
- 377
1
vote
1
answer
34
views
Partioning Mystery
Who has the wisdom to answer the following:
9 distinct marbles distrubted into 4 distinct bags with each bag receiving at least 1 marble,how many ways can this be done?
Thankyou for contributing!
...
- 59
1
vote
2
answers
47
views
Partioning/Enumeration
How many ways can one distribute
A) 15 Balls into 3 bags. Both bag and balls are distinct (labelled) and each bag must contain at least one ball.
B) 10 balls into 3 bags. again both bag and balls ...
- 59
1
vote
1
answer
124
views
Partitions of n with certain conditions
Let $p$ be prime and $n$ be any integer. Suppose $t=(n^{a_n}, \dots, 2^{a_2}, 1^{a_1}) \vdash n$, (i.e. $t$ is a partition of $n$, where we group repeated integers, so, for example, $2^{a_2}$ means ...
user39280
1
vote
1
answer
399
views
Cycle type of induced permutation
Let $m = \binom{n}{2}$ and $S_n, S_m$ be the symmetric groups, $S_n \subset S_m$. Let $\pi \in S_n$ and let $\pi$ have the the cycle type $[λ_1,λ_2,\dots,λ_k]$, $\lambda_1+\lambda_2+ \cdots+\...
- 8,204
5
votes
3
answers
4k
views
How many combinations of $3$ natural numbers are there that add up to $30$?
How many combinations of $3$ natural numbers are there that add up to $30$?
The answer is $75$ but I need the approach.
Although I know that we can use $_{(n-1)}C_{(r-1)}$ i.e. $_{29}C_2 = 406$ but ...
- 179
1
vote
1
answer
385
views
Integer Partition by Counting Repetition : Conjecture ??
I would like to find informations regarding this way of doing Integer Partitions or
this conjecture,
Suppose you have all the ordered partitions of 5:
5
4 1
3 2
2 2 1
3 1 1
2 1 1 1
1 1 1 1 1
Then ...
- 53
2
votes
0
answers
44
views
order of elements in a partition using Maple
I determined this whole partition but I just want to have the finer the partition
for example:
I have this
...
- 121
7
votes
1
answer
4k
views
Number of permutations with a given partition of cycle sizes
Part of my overly complicated attempt at the Google CodeJam GoroSort problem involved computing the number of permutations with a given partition of cycle sizes. Or equivalently, the probability of a ...
- 294