Is this cool with you?

gAr · 2011-07-25 21:42:10

Yes, me too!

bobbym · 2011-07-25 23:56:40

I was just working on a nice solution, I was amazed when it did not work! I mean it has to work, but it does not!

gAr · 2011-07-26 00:21:26

Oh, that's kind of depressing news.
Is that a recurrence formula?

For (3,4), I got 440 ways, don't know whether I made a mistake.

Ok, there was a mistake. After checking again, I get 323 ways?

Last edited by gAr (2011-07-26 00:32:33)

bobbym · 2011-07-26 00:33:46

Hi;

If it would have worked then there was an easier GF, a recurrence and an asymptotic form.

I am very sure the answer is 289. There is a generating function, that is what I am using to calculate the numbers.

gAr · 2011-07-26 00:59:12

Hi bobbym,

Okay, may be I did something wrong there.
I took those numbers and I hope this is the recurrence:

bobbym · 2011-07-26 01:13:36

Hi gAr;

I am sorry, but I never did figure out how to get Mathematica to run a two variable recurrence. Do you have some output?

gAr · 2011-07-26 01:20:34

Oh, not yet.

I thought you may already have some modules for such recurrences and posted before writing the code.

Everything done by hand till now, correct for the small values we have now.

I'll post back after calculating.

bobbym · 2011-07-26 01:29:30

Hi;

For some reason I can not get the command to work. I do not know how to fill in the initial conditions.

gAr · 2011-07-26 01:41:04

Hi bobbym,

Okay.
Anyway, it's solved.

Last edited by gAr (2011-07-26 01:43:09)

bobbym · 2011-07-26 02:04:32

Hi gAr;

gAr · 2011-07-26 02:09:12

Thanks!
Were you able to get the recurrence to work?
What's the g.f you have?

bobbym · 2011-07-26 02:13:36

Hi;

Nah, I am still unable to get it to work! There are plenty of examples but I am doing something wrong!

The GF is:

gAr · 2011-07-26 02:22:05

The g.f. looks cool. Thanks.

Can't you use a 2-D array in that, instead of trying the command?

bobbym · 2011-07-26 02:28:37

Hi gAr;

Yes, I could but I have to learn how to use that command sooner or later.

There is a nice asymptotic form for it also:

For when m = n.

gAr · 2011-07-26 02:31:57

Nice form indeed!
How to derive that?

bobbym · 2011-07-26 02:38:58

We have never had a problem on asymptotic analysis. I can only do a few of them that are the simplest. Complex analysis is used, much of it is like that integral we were working on.

Hopefully in the near future a question will pop up in "What do you think," that will require an asymptotic form.

gAr · 2011-07-26 02:42:09

Hmmm, I have never derived an asymptotic form, or seen the steps to derive one!

bobbym · 2011-07-26 02:48:04

The most well known of course is the Stirling approximation to n!. It is an asymptotic form.

Sometimes nothing but commonsense is involved.

Question: Quickly derive an approximation to this sum.

gAr · 2011-07-26 02:56:45

That was simple alright!
My immediate thought was n*n!, but I knew it was far larger to call it an approximation.

But aside, what were you trying in #879 ?

bobbym · 2011-07-26 03:01:05

Hi;

Are you up for a little background on this problem?

gAr · 2011-07-26 03:07:12

I'm going to take a break now, maybe 30 mins.
If you are available later, we can see.

Back soon!

Last edited by gAr (2011-07-26 03:07:38)

bobbym · 2011-07-26 03:08:02

Okay, see you then.

gAr · 2011-07-26 03:35:56

I'm back!

bobbym · 2011-07-26 03:40:53

The problem really is a self avoiding rook walk with some extra conditions. The rook in getting to (20,30) from (0,0) can move any number of vertices but can only move right and up. It amazingly is a bijection to the owed money problem!

gAr · 2011-07-26 03:49:01

Yes!

But you were saying it wasn't working?

Math Is Fun Forum

#876 2011-07-25 21:42:10

Re: Is this cool with you?

#877 2011-07-25 23:56:40

Re: Is this cool with you?

#878 2011-07-26 00:21:26

Re: Is this cool with you?

#879 2011-07-26 00:33:46

Re: Is this cool with you?

#880 2011-07-26 00:59:12

Re: Is this cool with you?

#881 2011-07-26 01:13:36

Re: Is this cool with you?

#882 2011-07-26 01:20:34

Re: Is this cool with you?

#883 2011-07-26 01:29:30

Re: Is this cool with you?

#884 2011-07-26 01:41:04

Re: Is this cool with you?

#885 2011-07-26 02:04:32

Re: Is this cool with you?

#886 2011-07-26 02:09:12

Re: Is this cool with you?

#887 2011-07-26 02:13:36

Re: Is this cool with you?

#888 2011-07-26 02:22:05

Re: Is this cool with you?

#889 2011-07-26 02:28:37

Re: Is this cool with you?

#890 2011-07-26 02:31:57

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Re: Is this cool with you?

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