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Tagged with integer-partitions set-partition
31
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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 $c$, ...
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Find a bijection between the $(n-1)$ paths and the $n$-paths which have no downramps of even length.
So here is the Question :-
A Dyck $n$-path is a lattice path of n upsteps $(x,y)$ $\rightarrow$ $(x + 1,y + 1)$ and $n$
downsteps $(x,y) \rightarrow (x + 1,y-1)$ that starts at the origin and never ...
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Consider the set $A=\{1,2,3,4,5,6,7,8,9\}$.A partition $\Pi $ of $A$ is collection of disjoint sets whose union is $A$
Consider the set $A=\{1,2,3,4,5,6,7,8,9\}$.A partition $\Pi $ of $A$ is collection of disjoint sets whose union is $A$. For example, $\Pi_1=\{\{1,2\},\{3,4,5\},\{6,7,8,9\}\}$ and $\Pi _2 =\{\{1\},\{2,...
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How many way to partition a set of n number into k subsets (empty subset is allowed)
I am working on finding the upper bound iterations of k-means algorithm. Many research show that the trivial upper bound is $O(k^n)$ since it can be shown that no clustering occurs twice during the ...
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149
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Find all combinations of numbers from {x1,x2,...,xn} that sum of to sum S
Given a list of some integers, I would like to find every combination that can be summed to some sum S.
For example for the sum S=16, and the list of integers I={3,4,5}, I'd expect to get:
5,4,4,3 (=...
2
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1
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98
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2-split of $n$ is $\left\{ \lfloor \frac{n}{2} \rfloor,\lceil \frac{n}{2} \rceil \right\}$. What about 3, 4, ...?
Clarification: $k$-split of $n$ is an ordered integer sequence $\left\{ a_1,\cdots,a_k \right\}\quad \text{s.t.}$
$0\le a_1\le\cdots\le a_k$
$a_1+\cdots+a_k=n$
${\left(a_k-a_1\right)}$ is minimized.
...
- 195
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Constructing a partition of a finite nonempty set from a partition of its cardinality
Let $E$ be finite nonempty set of cardinality $n$. Let $(k_i)_{i\in I}$ be a finite family of integers $>0$ such that
$$\sum_{i\in I} k_i=n.$$
Since $|E|=n$, there exists a bijection $x:[1,n]\...
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1
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115
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I can not find out a formula for this :
Between 1 and 45, (and included, 1 and 45) ;
How many --5 set combinations-- are there from 1 to 45 with a total of 155?
*What are these combinations ?
(PS: each number can only be written once )
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An interesting way of partitioning with inner ordered combinations
Assume $ K $ labeled blocks $ s_1, s_2, \dots, s_K $ ($ s_1 < s_2 < \dots < s_K $) that arrive sequentially and need to be accomodated as they arrive in $ N $ containers (partitions with ...
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2
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241
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Ways of distributing passengers in ships
I need help with the following combinatorial problem. There are $ K $ passengers and $ K $ ships. The passengers are denoted by $ U_1, U_2, \dots, U_K $. The objective is to find in how many ways the $...
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2
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1
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480
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Find Integer Partition using only integers belonging to S = { 1, 2, 3 }
I spent all afternoon looking for this but I wasn't able to find anything, so...
Is there a formula to know the NUMBER of partitions with a constraint on the integer domain ?
E.g.: Find the number of ...
- 158
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126
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What is the appropriate weight ($W_k$) (for two arbitrary partitions)?
I already asked a similar question, And from the answer I received, another question came to my mind.
A positive integer can be partitioned, for example, the number 7 can be partitioned into the ...
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Is this true for every partitioning?
I have two categories (category1 and category2 ) and The size of both categories is equal to each other. if we partition each categories arbibtrary .Is this proposition proven? or rejected?
$n_T \...
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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 ...
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2
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disjoint Partition of sets
Hello I'm a bit confused by what this definition means
$$DT_n = \{ \{C,D \} \mid C,D ⊆ S_n \text{ and } C \cup D = S_n \text{ and } C \cap D = \emptyset \} $$
where $S_n = \{1,2....n\}$ and n is a ...
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