For what it's worth, someone else on this list downloaded this paper for me. I read it, it did not even mention Pascal's triangle, and was instead about induction and probability.
So I went into facebook and went through the signup process for academia.org (which required I go through a variety of irrelevant screens - most of which I could skip but there was one irrelevant question which it insisted I answer), and downloaded a copy of the paper for myself. It was the same one. So now I am wondering why this paper was of interest? Because it had identities in it? But, also, at this point the discussion seems to have nothing to do with programming. Still, I'm more comfortable with Roger's original quoted quip "The numbers in Pascal's triangle satisfy, practically speaking, infinitely many identities..." than with Bo's "if you exclude the special cases, the remaining number of identities to learn is, practically speaking, finite" I do not even know what "special cases are" when talking about identities. Aren't they all special? That said, I feel that "infinite" is shorthand for "a tediously large number" and which suggests that any accurate discussion of whether something is or is not "infinite" can easily become tedious. -- Raul On Fri, Jun 7, 2013 at 10:23 AM, greg heil <[email protected]> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
