Questions tagged [integer-partitions]
Use this tag for questions related to ways of writing a positive integer as a sum of positive integers.
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Number of partitions into parts not greater than 9 [closed]
I'm looking for a closed-form formula for the number of partitions of integer $n$ into integer parts less than or equal to 9. Thanks.
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Number of different groups given a list of repeating digits
Suppose that you are given the list[1,1,2,2] . The different groups that can be formed with this list are -
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A question regarding partitions. [closed]
Number of partitions of n = p(n)
Number of partitions of n which has a part equal to 1 = p(n-1)
Number of partitions of n into k parts = p(n,k)
If for some k the following inequality holds
p(n,...
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Show that $p(n,k)=p(n-1, k-1)+p^2(n, k)$, Partition Theory
I'm struggling to prove this as I'm not sure how to do so with words/equations as opposed to visually.
$p^2(n,k)$ denotes the number of partitions of n having exactly k parts with each part greater ...
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How many ways can you express an integer as the sum of positive integers and each sum does not include any 2s? [closed]
I came up across this question while self-studying combinatorics. I am supposed to derive a recurrence relation, however I am not sure how to approach or even start this problem. The order matters.
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Find a minimal set whose elements determine explicitly all integer solutions to $x + y + z = 2n$
Is there a way to exactly parameterise all the solutions to the equation $x + y + z = 2n$, for $z$ less than or equal to $y$, less than or equal to $x$, for positive integers $x,y,z$?
For example, for ...
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Count the numbers of integer solutions of the ecuation $x_1 + x_2 + x_3 + x_4 = 21$ [duplicate]
How to count the number of nonnegative integer solutions to $x_1 + x_2 + x_3 + x_4 = 21$ such that $x_1$, $x_2$, $x_3$, $x_4 ≤ 7$
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list partitions (python) - why is the index out of range? [closed]
General problem: Using the elements of some list of length $m* n$, create a list with $m$ sub-lists, each of length $n$.
In my case, $m= 10 > n=3$.
The final output should be a list ("lis1&...
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