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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 ...
Walter White's user avatar
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 ...
Yvan's user avatar
  • 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 ...
Chouria Ali's user avatar
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 ...
xan's user avatar
  • 294

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