Bo isn't your article on these things (readable via Google docs) in
V1No.3 of the J journal at this address
http://www.journalofj.com/index.php/v1-no-3 and in pdf form from Google
here....
https://docs.google.com/gview?url=http://journalofj.com/images/pdf/V1.No.3.pdf&chrome=true
Phil
On 6/7/2013 3:28 AM, Bo Jacoby wrote:
@ Raul. I didn't know that downloading the PDF requested your password. Too
bad. What can be done?
- Bo
________________________________
Fra: Raul Miller <[email protected]>
Til: Programming forum <[email protected]>
Sendt: 22:19 torsdag den 6. juni 2013
Emne: Re: [Jprogramming] Finding repeated substrings
I would like to read the pdf.
But I do not feel like looking up my password.
--
Raul
On Thu, Jun 6, 2013 at 4:13 PM, Bo Jacoby <[email protected]> wrote:
@ Raul: Yes, one identity may have many proofs.
Why don't you want to download the PFD? What is the facebook account problem?
- Bo
________________________________
Fra: Raul Miller <[email protected]>
Til: Programming forum <[email protected]>
Sendt: 22:01 torsdag den 6. juni 2013
Emne: Re: [Jprogramming] Finding repeated substrings
Note that you can have many proofs for the same identity.
Also, I did not download your pdf, because I did not feel like signing
into my facebook account. So, for example, I do not know how your
identities treat the relationship between the pascal and sierpinski
triangles.
--
Raul
On Thu, Jun 6, 2013 at 3:37 PM, Bo Jacoby <[email protected]> wrote:
Yes, Roger, but if you exclude the special cases, the remaining number of
identities to learn is, practically speaking, finite. I have a collection of
identities in
http://www.academia.edu/3247833/Statistical_induction_and_prediction
to supplement those in Concrete Mathematics.
- Bo
________________________________
Fra: Roger Hui <[email protected]>
Til: Programming forum <[email protected]>
Sendt: 18:41 torsdag den 6. juni 2013
Emne: Re: [Jprogramming] Finding repeated substrings
To quote Graham, Knuth, & Patashnik, *Concrete Mathematics*, page 155: The
numbers in Pascal's triangle satisfy, practically speaking, infinitely many
identities, so it's not too surprising that we can find some surprising
relationships by looking closely.
The relationship you quoted, (>:x)!y ←→ +/x!i.y, can be generalized into a
theorem that I called Pascal's
Ladder<http://www.jsoftware.com/jwiki/Essays/Pascal%27s%20Ladder> (I
like that better than "Hockey Stick Theorem").
On Thu, Jun 6, 2013 at 9:18 AM, Bo Jacoby <[email protected]> wrote:
The theorem that 2!y is equal to +/i.y is a special case of the more
general theorem that (>:x)!y is equal to +/x!i.y
- Bo
________________________________
Fra: Roger Hui <[email protected]>
Til: Programming forum <[email protected]>
Sendt: 16:41 torsdag den 6. juni 2013
Emne: Re: [Jprogramming] Finding repeated substrings
There is a proof of a very similar theorem in section 1.4 of *Notation as
a
Tool of Thought <http://www.jsoftware.com/papers/tot.htm>*. (The
difference is that index origin is 1 in the paper.)
On Thu, Jun 6, 2013 at 6:44 AM, Raul Miller <[email protected]>
wrote:
Caution: this code can give an incomplete result. For example, I do
not believe it will find 'aabaab'. Rather than fix this, I'll defer to
other solutions in this thread (which I imagine properly address this
issue).
If anyone wants to take this code and fix it, the first instance of 2
-~/\ ] should be replaced with a mechanism that treats all
combinations of 2 (and not just adjacent pairs).
(And on that note, I Tracy Harms recently directed my attention to a
page with a beautiful proof that 2&! is +/@i. - that concept would be
useful, here, I think. I wish I had recorded the url of that page. But
the gist of my thought is that it should be possible to go from y and
a member of i.2!y to a unique pair of two numbers in the range i.y,
and that might be a nice way of implementing this "combinations of 2"
function.)
FYI,
--
Raul
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