This was the request for checkers. All the checking is now complete
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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----------------