Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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phanthanhtom
2013-06-15 01:24:17

Thanks

bobbym
2013-06-15 01:17:09

Okay, if I see anything different I will add it here.

phanthanhtom
2013-06-15 01:15:31

Again, I am looking for alternative names. I finished reading that twelvefold Wikipedia article. Formulae enough.

bobbym
2013-06-15 01:15:14

They are best done with exponential generating functions.

phanthanhtom
2013-06-15 01:14:22

In other words, partial permutation <=> k < n

phanthanhtom
2013-06-15 01:08:12

Yes you're right.

bobbym
2013-06-15 01:07:02

A partial permutation? Is that when you do not use all the elements of the set?

phanthanhtom
2013-06-15 01:05:03

Thank you. The Vietnamese names for them roughly translates to:
A. permutation
B. partial permutation
C. combination
D. partial permutation with repetition
E. combination with repetition
I am looking for formal and better alternatives, for I translate by my knowledge all these names, and it would be really important for BIMC.

bobbym
2013-06-14 23:09:25

Hi;

They are usually defined or named in terms of balls or objects in boxes or urns. I have never heard of anything else. That page is from Rota, it covers every type of combinatorics problem there is.

phanthanhtom
2013-06-14 23:06:31

Thanks, but I stress again that I need the official NAME, not the formulae.

bobbym
2013-06-14 21:59:08

Hi;

You might want to take a look here  when you have time.

http://en.wikipedia.org/wiki/Twelvefold_way

phanthanhtom
2013-06-14 21:31:28

And the formula for e is

phanthanhtom
2013-06-14 01:49:32

For k=3, n=5:
a. (a1, a2, a3, a4, a5) and (a1, a3, a4, a2, a5) are different solutions. All solutions contains all 5 objects.
b. (a1, a2, a3), (a1, a2, a4), (a1, a3, a2) are different solutions. (a1, a1, a4) is not, for repetition not allowed.
c. (a1, a2, a3) and (a2, a3, a5) are different solutions. (a1, a2, a3) and (a2, a3, a1) are the same. (a1, a3, a3) is not a solution.
I'm afraid I would be away now because it's late. I'll be back GMT 8:00 am. So I look for the answers then.
And I only need the words. I'm sure I know the formulae, just I don't have enough time.

bobbym
2013-06-14 01:47:29

Hi;

d, A way of choosing AND arranging k objects from S, repetition allowed, order matters.

Choosing k objects from n distinct objects with repetition and order matters is n ^ k

phanthanhtom
2013-06-14 01:39:05

d. For example if k=5, then (a1, a2, a2, a3, a3) would be a solution (repetition allowed), and it would be different from, say, (a1, a2, a3, a2, a3).
e. The above 2 would be the same solution, as order doesn't matter.