This was the request for checkers. All the checking is now complete --------------------------------------------------------------------- Last Update: Jan. 13, 1995 Note: The previous deadline of Dec. 15, 1994 has been extended to Feb. 14, 1995 (It would make a nice Valentine's Day present) First Written: Nov. 11, 1994 From: Doron Zeilberger, zeilberg@math.temple.edu To: Mathematicians at large, regardless of mathematical creed or heritage Re: Invitation to be a checker of one of the many (sub)^i-lemmas of my paper `Proof of the ASM conjecture' Greetings, Almost two years ago, I distributed the first version of the paper `Proof of the Alternating Sign Matrix Conjecture'. It was submitted to J. AMS, via Andrew Odlyzko. The dedicated referee(s) kept finding gaps, until, I was told, after the third version: The referee is a `bit' tired of finding errors in your proof, please don't resubmit it until it is real solid. This gave me the idea that a paper should be pre-refereed. Since the paper, that is now 78-page long(+references and exodion, that makes it 94-pages long altogether) is too long for any individual to be asked to check it (Surprisingly, Dave Bressoud, undertook this task, without being asked, and checked so far, about 60%, all by himself, and hopes to do the rest soon), I have perfected the tree structure' of the proof , that now makes it possible to have it `parallel-checked'. To every vertex ((sub)^i-lemma) in the proof tree, is needed at least one or more `checkers' whose responsibility it would be to check that the proof follows provided all the statements of the offspring-(sub)^(i+1)-lemmas are correct. Everything is conditional except, of course, for the leaf (sub)^i-lemmas. I feel that this is the way of the future for checking complex proofs (and also for designing them!) EVERYBODY IS WELCOME TO DO A (sub)^I-LEMMA. The list of checkers is only tentative. Pick any sublemma to your liking (the more the better). I would especially appreciate checkers in Acts III and IV. Why should you bother to do this job? 1) You would be doing me a big favor. 2)You get your name in the title page, right after my name, as one of the checkers. Since this is going to be a `historic' paper (If I do say so myself. Its significance would not be so much the proof itself, but the format in which it was written, and CHECKED, in other words, it is YOU, the checker, who is going to make it historic.), it should be a feather in your cap to be recognized as a checker. 3) As a token of gratitude, I will write for each of you, a short `bio', or rather epithet, that will be part of the paper, in the exodion. If you don't like what I wrote, you can send me a new version, when you submit your `checker's report'. WHAT DO HAVE TO DO IN ORDER TO BE A CHECKER? 1)Download the paper, following the following instructions: i) On your terminal type: ftp ftp.math.temple.edu followed by ENTER(CR) (Note that my old anon. ftp address: math.temple.edu is no longer valid) ii) To the login prompt, type anonymous iii) To the password prompt, respond with your e-mail address login@ Example : gauss@ (Assuming that you are Carl F.) iv) Type: cd pub cd zeilberg cd asm (Alternatively, type: cd pub/zeilberg/asm ) v) type get README get asm.tex (or asm.ps , if you wish) 2) Get a Hard Copy of the whole paper or the relevant parts by typing `lpr asm.ps' (if you have the .ps version) If you cannot afford 95 pages of printout, then, of course you can view it, assuming that you have a previewer. The most important files are: The title page: asm_title.tex (Make sure that your name is spelled correctly!) The introduction: asm_intro.tex (Required reading for all checkers, especially the Nomenclature and Crucial Facts sections) The exodion: asm_exodion.tex So you may `tex' only these 3 files for starters, by doing tex asm_exodion and then texprint asm_exodion (These commands may vary from system to system, if this does not work, ask any grad student, or secretary, how to tex and print a TeX file) and similarly for the other files. 3) Look at the Exodion. Locate your name, both in the skeleton of the proof tree, and in the bios section. Unless you are George Andrews or Dominique Foata (the `highest-level' checkers) your part is either one of the five sublemmas: 1.1 (Act I) 1.2 (Act II) 1.3 (Act III) 1.4 (Act IV) 1.5 (Act V), and for most of you, one of their descendants. So if you were charged with the checking of (sub)^r lemma 1.a_1.a_2. ... .a_r You only need (a portion of) Act a_1 , so it suffices that you only `tex asm_act' For example, suppose that you are Jamie Simpson. Then, your assigned portion is 1.2.1.2.1.1. So you only need to TeX file asm_actII.tex . 4) How to do the actual checking? Carefully read the proof of your assigned (sub)^i-lemma. Whenever you encounter a `son' (sub)^(i+1)-lemma, read its statement, of course, but NOT ITS PROOF, which is none-of-your-responsibility (they are other good souls whose duty it is.) Convince yourself that the reasoning is sound, and well-explained. 5) Submit your `Checkers Report', as soon as possible, but no later than Dec. 15, 1994 (or apply for an extension.) directly to me: zeilberg@math.temple.edu (Electronically, if at all possible.) I will collect all the reports and at the end show them to Andrew Odlyzko. You may use the convenient form below, or make your own. 6) Some checking tips: While I hope that you will splurge and print out all the 95 pages, in addition, or instead, you might want to create your own `Torah portion'. To do this first locate the Act that your (sub)^i-lemma is in, then, using the search command (for example ^S or ^R in emacs), search for your lemma. Then search for the word `sublemmas' and for each offspring sublemma delete its proof (That ends with the phrase `this ends the proof of sub...sublemma 1.\dots x_i',) SO search for this phrase, and delete all the text between `Proof:' and `This completes .. ,' ) Of course do not delete the statement. In a few cases there are cross-references (so the proof tree is not a perfect tree but a poset.) In this case make sure that there are no cycles. Some of the longer proofs have Cases and subcases, there the cases are not entirely self-contained and the checkers of the cases might have to read the whole (sub)^i-lemma, but are personally responsible only for their parts. You might also want to consult the Maple package ROBBINS, available by anon. ftp from the above site (ftp.math.temple.edu) but in directory pub/zeilberg/programs. See the top of p.3 (of the introduction, that is in file asm_intro.tex) for instructions. 7) What if you are too busy, or for other reasons, do not believe that you will be able to do your share by Dec. 15? Then: Please try to find a colleague or a grad student to volunteer to do your part, and let me know of this change. IF YOU ARE UNABLE/UNWILLING TO BE A CHEKER AND UNABLE/UNWILLING TO FIND A SUBSTITUTE PLEASE LET ME KNOW RIGHT AWAY! 8) I hope very much that you will be able to participate in the checking process. Please let me know whether you would be able to participate ( andI would be glad to answer any questions that you might have.) If the answer is yes, you may use the convenient form below (or make your own.) and E-mail it to me ASAP but no later than Dec. 15. If you do (and no irreparable gaps would be found) then your name will remain for ever after in the list of checkers in the title page, and your `bio' will be included in the Exodion, like it is now. (In the likely event that JAMS will refuse to paper-publish the Exodion, there would still be a pointer to it, so that anyone can ftp it. At any rate, I will insist on the list of checkers in the title page.) Best Wishes, and Thanks in advance! Doron -------begin checker's form--------------------------- (Fill in the blanks [], and delete the superfluous parts) Dear Doron, I have now completed checking (sub)^[]lemma [ ]. To the best of my judgment, it is correct, provided all its offspring (sub)^[]-lemmas are correct. Needless to say, I don't know (and don't care!) whether the proofs of these offspring (sub)^[]-lemmas are actually correct. and (optional) I have found the following typos or other errors:[ ] and (optional) I have the following suggestion to improve the exposition:[ ] OR Sorry, your argument is unconvincing, but I found a way to fix it as follows: [ ] OR Sorry, your argument is unconvincing, and I don't see how to fix it. Best Wishes, [ ] P.S. I like the epithet you wrote for me OR I rather write my own, which is enclosed below (Up to four lines, in eight Roman, please.):[ ] ---------end checkers form----------------