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 >>>>>>>> >>>>>>> ---------------------------------------------------------------------- >>>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>>>> >>>>>>> >>>>>> ---------------------------------------------------------------------- >>>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>>> >>>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
