Bo Ah then, perhaps for the benefit of us ~non_farcebookers and in the hopes of obtaining an ~open-utrality for your efforts you can find some spot to place the paper? Eg a ~dropbox_account?
---~ http://u.tgu.ca/non_farcebookers http://i.tgu.ca/open-utrality http://i.tgu.ca/dropbox_account greg ~krsnadas.org -- from: Bo Jacoby <[email protected]> to: "[email protected]" <[email protected]> date: 7 June 2013 06:55 subject: Re: [Jprogramming] Finding repeated substrings Philip, yes, but the JoJ-article does not include the proofs. -- Fra: Philip Hunt (USA) <[email protected]> Til: [email protected] Sendt: 14:58 fredag den 7. juni 2013 Emne: Re: [Jprogramming] Finding repeated substrings >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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
