All Questions
Tagged with integer-partitions permutations
34
questions
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
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
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
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
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
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
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
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.
$$10+10+10+...
- 23
2
votes
3
answers
1k
views
Number of ways of cutting a stick such that the longest portion is of length n
We are given a stick of length $L$ (say). We make cuts such that the longest piece is of length $n$ (say) at most.
What are the minimum number of pieces we will get and in how many ways this can be ...
2
votes
0
answers
44
views
order of elements in a partition using Maple
I determined this whole partition but I just want to have the finer the partition
for example:
I have this
...
- 121
1
vote
1
answer
359
views
How many partitions of $n$ are there?
Considering a partition to be an ordered $n$-tuple $(m_1, m_2, m_3, ..., m_n)$ with all the numbers $m_i$ natural, $m_1 \le m_2 \le m_3 \le ... \le m_n$, and $m_1+m_2+...+m_n=n$: how many of those $n$-...
- 851
1
vote
2
answers
1k
views
The number 3 can be written as $3$, $2+1$, $1+2$ or $1+1+1$ in four ways. In how many ways can the number $n$ be written?
Attempt
Let $x$ be any variable
$X+0=n ; X+Y=n ; X+Y+Z=n ; \dots; X+Y+Z+A+\dots=n$ (sum of n-1 terms); $1+1+1+.......+1=n$ (sum of n terms).
So total number of ways=
$$(n-1) C (1-1)+(n-1) C (2-1)+\...
- 85
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
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