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#26 2006-03-05 20:16:05

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

I verified the results and it seems that:


too. So we get new formula for the stirling numbers!


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#27 2006-03-09 05:54:31

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

I'll try to generalize the result for higer dimentions.


IPBLE:  Increasing Performance By Lowering Expectations.

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#28 2006-03-09 06:10:56

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

Here's analytic definition of p_k (n) in Mathematica language:
p := If[#1 == 1, #2(#2 + 1)/2, Sum[i #0[#1 - 1, i], {i, 1, #2}]] &

Example:
p[1,n]=n(n+1)/2


IPBLE:  Increasing Performance By Lowering Expectations.

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#29 2006-03-09 06:31:52

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

Strange.
Here's a table of the denominators of p_i (n) for i =1 to 20.
Can someone tell me something about this sequence?

2


24


48


5760


11520


11520


2903040


5806080


1393459200


2786918400


367873228800


735746457600


24103053950976000


48206107901952000


578473294823424000


1156946589646848000


9440684171518279680000


18881368343036559360000


271211974879377138647040000


542423949758754277294080000

It seems to be very irregular.


IPBLE:  Increasing Performance By Lowering Expectations.

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#30 2006-03-09 06:33:24

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

note that the 5th and 6th term are equal!!!


IPBLE:  Increasing Performance By Lowering Expectations.

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#31 2006-03-09 22:25:35

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

Here's more general proposition:


for all natural k,n


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#32 2006-03-09 22:58:12

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

Now I'm veryfing the proposition for n,k <=100. It will take some time.


IPBLE:  Increasing Performance By Lowering Expectations.

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#33 2006-06-09 15:43:15

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,552

Re: Pure problem

Ansette wrote:

we have to try and place these individual boxes into a large parcel that must be rectangular with no free space, though the dimensions are irrelevant.. kind of like a three-dimensional tetris..

On the subject of tetris, here's an online game of it: http://www.crazybone.com/onlinegames/li … p?link=232


igloo myrtilles fourmis

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#34 2006-06-10 02:49:50

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Pure problem

Only game???
Where's the maths?


IPBLE:  Increasing Performance By Lowering Expectations.

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