Any recommendations?

bobbym · 2012-09-15 03:14:44

Let's say we want the 8th unrestricted partition or p(8).

We generate some generalized pentagonal numbers first. We use:

with n = -4, -3, -2, -1, 0, 1, 2, 3, 4 why we go from -4 to 4 will be clearer when you do some these yourself. Anyway, this generates the sequence

you only keep numbers whose absolute value is < 8 and do not equal 0. So the sequence becomes:

Now the absolute value of each of those numbers is subtracted from 8 to get:

p(8) = p(8-1) ± p(8-2) ± p(8-5) ± p(8-7)

that becomes

p(8) = p(7) ± p(6) ± p(3) ± p(1)

To get the correct signs instead of ± , look at the sequence. If the number that is subtracted from 8 is positive then the ± becomes + if it is negative then it becomes negative.

Agnishom · 2012-09-15 03:31:21

Wikipedia provides this program:

 pentagonal = lambda n : n*(3*n-1)/2
 
 def generalised_pentagonal(n): # 0, 1, -1, 2, -2
     if n < 0: return 0
     if n%2 == 0: return pentagonal(n/2+1)
     else: return pentagonal(-(n/2+1))
 
 pt = [1]
 for n in range (1, 1000+1):
     r = 0
     f = -1
     i = 0
     while 1:
         k = generalised_pentagonal(i)
         if k > n:
             break
         if i%2==0: f = -f
         r += f*pt[n - k]
         i += 1
     pt.append(r)
 
 print pt

I just replaced the condition of the loop with what I require
I got the answer within a few seconds

bobbym · 2012-09-15 05:09:23

Hi;

Did you understand what I did in post #26?

Agnishom · 2012-09-15 17:15:57

Yes!
1. To calculate a partition, we have to calculate(some of) the previous partitions.
2. We need to know that p(1) = 1

I can understand how we use it, but not the principle behind it

Last edited by Agnishom (2012-09-15 17:17:43)

bobbym · 2012-09-15 17:24:00

Hi Agnishom;

Have you seen my signature? That is from a top mathematician. If he has trouble understanding some things what can be expected of us? Fortunately, if you understand the mechanics of a math technique or algorithm you can then use it. I gave you the how it works stuff, the why it works is much tougher and I do not fully understand it.

Incidentally, I only showed this rather inefficient technique as a means to solve that specific problem.

Agnishom · 2012-09-15 18:42:26

Grand Idea!

Agnishom · 2012-09-17 16:48:13

By the Way, Once upon a time you had a signature about wastage of time and money. Would you please explain that?

bobbym · 2012-09-17 22:18:37

Hi Agnishom;

I do not remember that one, can you give me a hint?

Agnishom · 2012-09-18 00:28:52

Something like this:
How often do I see money and time being wasted..............
Then You told something about calculations....

bobbym · 2012-09-18 06:21:26

Hi Agnishom;

That is very good that you remember that much. I wished I could remember the
entire quote and who said it. If I do I will explain.

Agnishom · 2012-09-19 00:10:04

At that time I never understood what they were as I did not have the concept of Signatures. They seemed very confusing to me

Big discoveries are protected by public incredulity.

What is the meaning of public incredulity?

anonimnystefy · 2012-09-19 01:15:31

It means, that big discoveries are looked at with disbelief by the general public.

bobbym · 2012-09-19 02:06:53

Hi all;

That is close.

anonimnystefy · 2012-09-19 02:20:54

How close?

bobbym · 2012-09-19 02:24:56

Pretty close...

anonimnystefy · 2012-09-19 02:26:55

Where do the La***ta files come in?

bobbym · 2012-09-19 02:34:04

There is a difference between how Marshall McLuhan and I interpret that quote.
I did not know him personally or attend the parties he did or hang in his social set.
Therefore I do not know what secrets he was exposed to.

Math Is Fun Forum

#26 2012-09-15 03:14:44

Re: Any recommendations?

#27 2012-09-15 03:31:21

Re: Any recommendations?

#28 2012-09-15 05:09:23

Re: Any recommendations?

#29 2012-09-15 17:15:57

Re: Any recommendations?

#30 2012-09-15 17:24:00

Re: Any recommendations?

#31 2012-09-15 18:42:26

Re: Any recommendations?

#32 2012-09-17 16:48:13

Re: Any recommendations?

#33 2012-09-17 22:18:37

Re: Any recommendations?

#34 2012-09-18 00:28:52

Re: Any recommendations?

#35 2012-09-18 06:21:26

Re: Any recommendations?

#36 2012-09-19 00:10:04

Re: Any recommendations?

#37 2012-09-19 01:15:31

Re: Any recommendations?

#38 2012-09-19 02:06:53

Re: Any recommendations?

#39 2012-09-19 02:20:54

Re: Any recommendations?

#40 2012-09-19 02:24:56

Re: Any recommendations?

#41 2012-09-19 02:26:55

Re: Any recommendations?

#42 2012-09-19 02:34:04

Re: Any recommendations?

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