All Questions
Tagged with integer-partitions permutations
34
questions
3
votes
1
answer
852
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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
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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
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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
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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
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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
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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
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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
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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
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275
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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
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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
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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
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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
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47
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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
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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
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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+\...
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