HDTenEightyP/NetNews huggingface dataset:
From: mitchell@math.ufl.edu (Bill Mitchell)
Newsgroups: sci.math,sci.logic
Subject: Set Theory Eprints
Date: 6 Apr 92 21:07:58 GMT
Article-I.D.: leadbell.MITCHELL.92Apr6170758
Organization: University of Florida Department of Mathematics


  SET THEORY EPRINTS has arrived!!!

						 (  ...finally)


Are you tired of receiving preprints you don't really care about in
the mail, while the ones you wanted to see never arrive?

Are you tired of mailing dozens or scores of preprints, never being
sure if the people who are REALLY interested are on your mailing list?

Are you tired of sitting for months with results which you would like
to get out, but which are taking forever to reach that polished state
which would justify sending them out to your mailing list, let alone
submitting them for publication?

A solution is at hand:  SET THEORY E-PRINTS.

You can electronically submit abstracts and TeX source for papers.
The abstracts will be collected together and mailed out daily to
subscribers to SET THEORY E-PRINTS, and the tex source for the papers
will be available to anyone on the net, either by electronic mail or
by ftp.

________________________________________________________________


  To SUBSCRIBE to this service, send an email message to
"listserv@math.ufl.edu" with the following line as the text of the
message:

   add settheory

If you have expressed interest in response to my previous mailing, and
I didn't misplace your reply, then I will have added you to to list
In this case you will have received (or will shortly receive) an
acknowledgment.

  For FURTHER INFORMATION on this service, including instructions for
submitting abstracts  and for submitting or obtaining papers, send an
email message to the same address with the following line as text.  (If
you subscribe then you will automatically receive this information.)

   FAQ settheory


________________________________________________________________


  Bill Mitchell
    Dept of Math., The University of Florida
    mitchell@math.ufl.edu

--

  Bill Mitchell
    Dept of Math., The University of Florida
    mitchell@math.ufl.edu
Newsgroups: sci.math
From: allenk@bullyrag.ugcs.caltech.edu (Allen Knutson)
Subject: Re: Erdos, the pronunciation
Organization: California Institute of Technology, Pasadena
Date: Sun, 12 Apr 1992 20:49:26 GMT

bdm@cs.anu.edu.au (Brendan McKay) writes:


>In article 15616@wheaton.wheaton.edu, poynor@wheaton.edu (George V. Poynor) writes:

>Here is the correct pronunciation (of Erdos's name)
>as taught me by Erdos himself.  After writing it down, I verified it
>with another Hungarian mathematician who has been a close friend of
>Paul's for more decades than she would admit.

>  Er  : similar to the English word "air" but the "r" is rolled briefly.
>        It is hard for English speakers like me to roll the "r" without
>        creating a pseudo-syllable between this one and the next;
>        however this is essential.  

>  dos : (there is a long Hungarian umlaut on the "o", in TeX: \H)
>        the sound is similar to the English "ersh" though not exactly.
>        The long accent makes the "er" fairly long. 

>  The accent is on the first syllable.
					(as with _all_ Hungarian words)

>His first name is actually Pal (accent on the "a") pronounced "Pahl",
>but practically everyone calls him "Paul" with the English pronunciation.

Most of the people I ran into in Hungary (who knew him) called him
"Pali bacsi" (polly botchi), meaning "Uncle Paul".		Allen K.
From: luzeaux@roma.berkeley.edu (Dominique Luzeaux)
Newsgroups: sci.math
Subject: Re: nonexistance of counterexample -> existance of proof?
Date: 9 Apr 92 21:16:06 GMT
Article-I.D.: pasteur.1992Apr9.211606.22882
Reply-To: luzeaux@roma.berkeley.edu (Dominique Luzeaux)
Organization: University of California

In article <31475@sdcc12.ucsd.edu>, ec120wee@sdcc4.ucsd.edu (Anthony
Minkoff) writes:
|> He made the statement "If no counterexample exists, then a proof
|> exists."  Of course, I can't prove him wrong 
|> Anyway, the story continues...  I then tried to present an example
|> of a theorem with no proof, and no counterexamples.  First, I made
|> the claim that there must be real numbers with no finite expression.
|> (A finite expression does not necessarily imply a finite expansion.
|> For example, sqrt(2) is a finite expression.)  I offered the
|> following proof:
|> 
|> Any finite expression can be encoded as a finite sequence of bits,
|> according to the following scheme:  Begin the sequence with an ASCII
|> text description of how to decode the part of the sequence following
|> the description.  (Of course, the entire description may be the
|> ASCII text.)
|> Since a one-to-one correspondence can be established between finite
|> sequences of bits and integers, but not between reals and integers,
|> there are reals with no finite expressions.

You have to assume that your coding is an injection

|> Should this be posted to a philosophy newsgroup?

No, sci.math is all right, or sci.logic
Anyway, nonexistence of counterexamples does not imply existence of proof.

As you mentioned it, Goedel built a formula which was true but could not
be proved in the theory where this formula was built. Your problem points
at the fact that truth and provability are different, because provability
(with the logical meaning, I mean following Hilbert's scheme) implies a
FINITE number of steps in your proof playing with axioms and rules of 
inference and theorems which were already proved in this manner.
From: luk@ohstpy.mps.ohio-state.edu
Newsgroups: sci.math
Subject: eigenvalue PDE
Date: 14 Apr 92 21:44:56 GMT
Article-I.D.: ohstpy.12070.29eb1a18

Does anybody have the experience solving the following partial differential
eigenvalue equation:

L[\phi(x,y)]=E*\phi(x,y)   where E is eigenvalue and L is operator defined by 

A*(\partial_{x,x}+\partial_{y,y})+ i*B*(x*\partial_{y}-y*\partial_{x})+
C*(x**2+y**2)=0

A,B, and C are real constant and i is imaginary sqrt(-1). 
Newsgroups: sci.math,comp.theory
From: narendra@ithaca.cs.wisc.edu (B. Narendran)
Subject: Coloring hypergraphs
Keywords: hypergraphs, colorings 
Organization: University of Wisconsin, Madison -- Computer Sciences Dept.
Date: Tue, 14 Apr 1992 17:12:57 GMT

Can someone point me to any known results for the following problem:

Given the complete k-hypergraph (all hyperedges are of size k) of n
vertices, and a k-coloring of its vertices, a hyperedge of the 
graph is said to be "covered" by the coloring if no two vertices
of that hyperedge are colored by the same color. What is the minimum
number of colorings that are needed to cover all the hyperedges?

A probabilistic result of Erdos and Kleitman from '68 implies that
O(log n) colorings suffice. Does anyone know of a constructive version
of this result?  (Note that for k=2, a simple binary labeling of the 
nodes gives the required colorings.)

Thanks...

- Narendran.

------------------------------------------------------------------------------
 narendra@cs.wisc.edu			B. Narendran
					Computer Sciences Dept.
					University of Wisconsin-Madison.
					1210 W Dayton St
					Madison WI 53706.
------------------------------------------------------------------------------
-- 

------------------------------------------------------------------------------
 narendra@cs.wisc.edu			B. Narendran
					Computer Sciences Dept.
					University of Wisconsin-Madison.
					1210 W Dayton St
					Madison WI 53706.
------------------------------------------------------------------------------
Newsgroups: sci.math.research
From: larsen@mace.princeton.edu (Michael Larsen)
Subject: Re: projective representations
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Princeton University
Date: Fri, 3 Apr 1992 15:59:55 GMT
X-Administrivia-To: sci-math-research-request@uiuc.edu

In article <ARA.92Apr2004750@camelot.ai.mit.edu> ara@zurich.ai.mit.edu (Allan Adler) writes:
>
>
>Let G be the simple group of order 168. G has an irreducible representation
>of dimension 6 over the field with 2 elements. Let A be the elementary
>abelian group of order 2^6=64 that G acts on via this representation.
>Let H be the semidirect product of G and A. 
>
>Does H have an faithful irreducible complex projective representation of
>degree 8 ?
>
The short answer is yes.  The point, as the original poster probably
surmised, is to use a characteristic 2 version of the Weil representation.

Explicitly, let V denote a vector space of dimension 3 over the field
with 2 elements.  Let C[V] denote the complex group ring of V.  We can
view the dual space $V^*$ as a space of complex functions on V via
the sign character on Z/2Z.  Therefore V^* acts on C[V] by multiplication,
while V acts on C[V] by translation.  The two actions don't quite commute,
but they do give rise to a projective (8-dimensional) complex representation
of V x V^*.  This representation lifts to an actual representation
on the Heisenberg group H (central extension of V x V^* by Z/2Z with
2-cocycle given by the natural pairing (a,a*) x (b,b*) --> a*(b) + b*(a).)
The character of the representation rho is easy to calculate; it is zero
on non-zentral elements, 8 on the identity, and -8 on the other
central element.  Since the order of the group is 128, rho 
is irreducible.  On the other hand, any automorphism of the Z/2Z-vector
space W = V x V^* which preserves the symplectic form on W gives
rise to an automorphism of H, and conjugating by
this automorphism does not change the character of rho.
Thus the elements of Sp(W) intertwine rho with itself.  By Schur's lemma,
the semidirect product of Sp(W) by H admits a projective 8 dimensional
representation (which in fact is an actual representation if you replace
Sp(W) by Mp(W).)  The restriction of the representation to Sp(W) gives
the Steinberg representation.  

To solve the given problem, we realize the 168-group as the Levi component of 
a maximal parabolic subgroup of Sp(W) and restrict.

						-Michael Larsen

P.S.  Has anyone worked out a theory of dual reductive pairs over finite
fields?

Newsgroups: sci.math.research
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math.research
Subject: Re: projective representations
Date: 7 Apr 92 16:42:22 GMT
Organization: M.I.T. Artificial Intelligence Lab.
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

In article <1992Apr3.160009.8584@Princeton.EDU> larsen@mace.princeton.edu (Michael Larsen) writes:


   P.S.  Has anyone worked out a theory of dual reductive pairs over finite
   fields?



Roger Howe has a paper entitled "Invariant Theory and Duality for Classical
Groups over Finite Fields, with Applications to their Singular Representation
Theory".  It is unpublished, although apprently quite influential, and I have 
heard that someone (Paul Sally?) was going to include it in a volume of
influential unpublished papers by various authors.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: Toda lattices
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
Date: Thu, 9 Apr 1992 18:35:01 GMT
X-Administrivia-To: sci-math-research-request@uiuc.edu



If you know how to associate a Toda lattice to an extended Dynkin diagram
and would not mind explaining some very elementary things to me as well, please
contact me.

Allan Adler
ara@altdorf.ai.mit.edu
From: msapir@hoss.unl.edu (Mark V. Sapir)
Newsgroups: sci.math.research
Subject: representations of partially ordered sets
Keywords: partially ordered sets, representations
Date: 14 Apr 92 20:04:38 GMT
Article-I.D.: unlinfo.1992Apr14.200452.10978
Organization: University of Nebraska - Lincoln
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu

Is it true that every partially ordered set of height 2 is representable
by subspaces of a 6-dimensional vector space?

Here:

   Height 2 means that every chain has at most three elements,
   A partially ordered set T is representable in a vector space V if there
exists a 1:1 mapping from T to the set of subspaces of V which preserves the
order.

In particular, every finite geometry is a partially ordered set of height
2. Is it possible to represent every finite geometry in a 6-dimensional
space (points should go to lines, lines should go to 3- or 2-dim. subspaces).

There exists a partially ordered set (even a semilattice) of height 2 which 
can not be represented in a 5-dim. space. I could not find this example in
the literature so I had to construct it myself.

I know that there is a lot of results in algebraic topology, in the theory of
representations of associative algebras, in combinatorics etc concerning 
representations of partially ordered sets. It would be strange if nobody
knows the answer to my question.

Mark V. Sapir
Newsgroups: sci.math.research
From: jbaez@BOURBAKI.MIT.EDU (John C. Baez)
Subject: Generalized Temperley-Lieb algebra?
X-Submissions-To: sci-math-research@uiuc.edu
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 13 Apr 1992 16:23:22 GMT
X-Administrivia-To: sci-math-research-request@uiuc.edu

Thanks very much, all, for the responses to my "Knotty Problems."  The
returns haven't all come in yet, but if anyone who wrote me would like
to know what everyone *else* had to say about those questions, just
email me.  

Okay, now for something slightly different.   Just as for every group
there is a group algebra, for every monoid there is a monoid algebra.
As far as I recall, the Temperley-Lieb algebra is the monoid algebra
based on the monoid of "tangles on n strands"; which is an extension of
the concept of braids where in addition to crossings:


\   /
 \ /
  \
 / \
/   \


and their inverses, one has things like


\   /
 \_/

  _
 / \
/   \


which don't have inverses.  These satisfy all sorts of charming
relations.  I may have my terminology mixed up a bit here, but I *don't*
need more information on the Temperley-Lieb algebra per se because I
have lots of references on it.  What I'm looking for is somewhat
different.  Namely, what do people call the algebra corresponding to the
monoid generated by crossings, elements like

\   /
 \_/
        
and elements like

  _
 / \
/   \  

Of course the latter two do not conserve the number of strands.

I suppose one could call this simply an "unoriented tangle algebra".
What precisely are the relations for it?  How about the analog for
oriented tangles?  It comes up in the Reshetikhin-Turaev
approach to constructing knot, link, and tangle invariants from quantum
groups (or rigid braided tensor categories).  But are there any good
references on "tangle monoids" and tangle monoid algebras per se?








Newsgroups: sci.math.research
From: Allan Adler <ara@zurich.ai.mit.edu>
Subject: centralizers of semisimple elements
X-Submissions-To: sci-math-research@uiuc.edu
Organization: M.I.T. Artificial Intelligence Lab.
Date: Tue, 7 Apr 1992 15:04:57 GMT
X-Administrivia-To: sci-math-research-request@uiuc.edu


Let G be a finite group of Lie type. How does one describe the semisimple
conjugacy classes of G and how does one describe the centralizer of a
semisimple element ?

The answer to this is given in Carter's book Finite Groups of Lie Type
in Chapter III. However, in practice the computation of the centralizers
seems unnecessarily complicated since it depends on an examination of the
entire root system for G.

If G is GL(n), one can first diagonalize a semisimple element over the
algebraic closure, then group the identical eigenvalues together on
the diagonal and then easily compute the centralizer. In effect, one
is choosing the element first and the ordering of the roots next. This
seems easier than obtaining a collection of roots whose root subgroups
a priori generate the centralizer along with the torus and certain
Weyl group elements and trying to recognize the group they generate.

For example, with GL(n), if one removes those vertices of the
Dynkin diagram that are not trivial on the semisimple element
(assuing the roots were ordered as above), what's left is the
Dynkin diagram of the centralizer.

To what extent can this be done in general ?

Allan Adler
ara@altdorf.ai.mit.edu

Newsgroups: sci.math.research
From: mvelezre@athena.mit.edu (Miguel . Velez-Reyes)
Subject: Lower Bound on the conv. rate of Gauss Seidel
X-Submissions-To: sci-math-research@uiuc.edu
Organization: Massachusetts Institute of Technology
Date: Thu, 9 Apr 1992 16:57:51 GMT
X-Administrivia-To: sci-math-research-request@uiuc.edu

Does anyone knows of a lower bound for the convergence rate of the
Gauss-Seidel algorithm for a positive definite matrix. It always
converges for positive definite matrix however, I am looking for
information on its dependence on the conditioning of the matrix.

Something like if the matrix is ill-conditioned then the slower the
convergence rate. Or is it independent of the conditioning?

Some sort of relation can be shown for consistently ordered matrices
where the asymptotic convergence rate is the square of that for Jacobi's
method and the later is equal to

	\rho(GS)=\rho(J)^2=((c(A)-1)/(c(A)+1))^2
where

	c(A) = cond(S*A*S)

and S is a scaling matrix that makes all diagonal elements of S*A*S
equal to one.

When the matrix is not consistently ordered then the expression above is
a lower bound on the convergence of Jacobi's method but in general
Jacobi's method does not necessarily converge for arbitrary positive
definite matrices while Gauss-Seidel does.

ANy ideas or suggestions, I will post a summary if I get enough
responses.



Miguel Velez

mvelezre@athena.mit.edu


Newsgroups: sci.math,comp.theory
From: mab@wdl39.wdl.loral.com (Mark A Biggar)
Subject: Re: factorial function
Organization: Loral Western Development Labs
Distribution: usa
Date: Mon, 13 Apr 1992 16:40:44 GMT

In article <1992Apr11.064011.15286@ringer.cs.utsa.edu> djimenez@ringer.cs.utsa.edu (Daniel Jimenez) writes:
>If we can calculate n! mod 100000, we can know the last few digits
>of n!, assuming the algorithm lends itself to modulus like
>exponentiation does.

But you can calculate n! mod 100000 in O(1) time for all n >20. :-)

--
Mark Biggar
mab@wdl1.wdl.loral.com
From: smith@gramian.harvard.edu (Steven Smith)
Newsgroups: sci.math
Subject: Re: factoid about new prime
Date: 7 Apr 92 15:22:15 GMT
     <1992Apr1.201324.25572@linus.mitre.org>
Organization: Harvard Robotics Lab, Harvard University

In article <1992Apr1.201324.25572@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:

> In article <3987@crl.LABS.TEK.COM> scott@ferrari.LABS.TEK.COM (Scott Huddleston) writes:
> :It was mentioned on CNN that the new prime number discovered
> :recently is four times bigger then the previous record.
> :
>
> This is a (slight) exaggeration. 756839/216091 = 3.5024 times as big.

Pardon me, but

                756839
               2       - 1                                          162781
               -----------  ~=  2.33397019895780128135136676956 x 10
                216091
               2       - 1

which is larger than four.  It appears that CNN was conservative in
their report.

Steven Smith
From: sasrdt@shewhart.unx.sas.com (Randall D. Tobias)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 6 Apr 92 21:27:52 GMT
Article-I.D.: unx.1992Apr6.212752.8308
    <STROMME.92Apr6130830@jeeves.math.utah.edu>
Organization: (none)
Originator: sasrdt@shewhart.unx.sas.com
X-Bytes: 1622

In article <STROMME.92Apr6130830@jeeves.math.utah.edu>, stromme@math.utah.edu (Stein Stromme) writes:
|> In article <1992Mar31.171529.4532@linus.mitre.org> bs@gauss.mitre.org (Robert D. Silverman) writes:
|>    In article <1992Mar31.074735.28595@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
|>    >>No, Erdos only offers money for his own problems.
|>    >
|>    >Pardon my ignorance. Who is this Erdos dude?
|>
|>    You're joking right???  April 1 is tomorrow, not today, right???
|>
|>    This must be a joke. How can anyone who reads or posts to this newsgroup
|>    not know who Paul Erdos is???
|>
|>    I can understand Joe Blow off the street not knowing, but how can anyone
|>    with an interest in math [evidenced by the fact that he reads this group]
|>    not know??
|>
|>
|>
|>    --
|>    Bob Silverman
|>    These are my opinions and not MITRE's.
|>    Mitre Corporation, Bedford, MA 01730
|>    "You can lead a horse's ass to knowledge, but you can't make him think"
|>
|>
|> Come on, Bob, as a reader of this group you must have noticed that its
|> contributors range from the professional to the not-so-professional.
|> Why not just answer the question? After all, the poster says "Pardon
|> my ignorance", and then he does not deserve to be run over like that.
|>
|> Stein

Seconded.
-- 

Randy Tobias               SAS Institute Inc.     (919) 677-8000 x7933
sasrdt@dev.sas.com         SAS Circle             (919) 677-8224 (Fax)
72450.2545@compuserve.com  Cary, NC   27512-8000

 ... just my $(-exp(2*sqrt(-1)*arcos(0))/(((2**(2 + 1)) - 1)**2 + 1)).
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Question on Connectedness
Keywords: Topology
    <1992Apr15.94411.12025@ms.uky.edu>
Organization: University Of Kentucky, Dept. of Math Sciences
Date: Wed, 15 Apr 1992 13:49:41 GMT
X-Bytes: 

In article <1992Apr15.94411.12025@ms.uky.edu> cyeomans@ms.uky.edu (Charles Yeomans) writes:
>In article <36937@gremlin.nrtc.northrop.com> jbarnett@nrtc.northrop.com (Jeff Barnett) writes:
>>Is the following true in the topology of Euclidean n space:
>>
>>P is a collection of non-empty (pairwise) disjoint closed sets.  P is
>>a partition of S.  Claim -- if S is connected, then the cardinality
>>of P is either 1 or uncountable.
>>
>>Jeff
>>
Damn.  I read the real question and now I get the point.
>Charles Yeomans
>cyeomans@ms.uky.edu
>yeomans@austin.onu.edu
>
>


Newsgroups: sci.math,sci.crypt
From: gindrup@math.okstate.edu (Eric `'d'kidd' G..)
Subject: Re: Tangent^2 re: Mersenne
Organization: Oklahoma State University, Math Department
Date: Fri, 10 Apr 1992 20:50:39 GMT

In article <1992Apr6.231148.10786@husc3.harvard.edu> elkies@ramanujan.harvard.edu (Noam Elkies) writes:
>
>Whoa --- one also needs that half the primes p *such that 2p+1 is prime*
>are congruent to 1 mod 4; it is still a big open problem to prove that
>there are infinitely many such p to begin with!  I certainly have no
>reasonable doubt that there are infinitely many, and that they are
>correctly distributed mod 4, but a "Theorem!" it isn't.
>

I belive that Whitehead showed (shewed) that (primes less than n that are
congruent to 1 mod 4) - (primes less than n that are congruent to 3 mod 4)
has infinitely many zeroes and then went on to show that the smallest one
was (upper) bounded by some ridiculously unhelpful integer.  Later, other
work was done to reduce the bound to something merely useless...  :-)

-- Eric Gindrup ! gindrup@hardy.math.okstate.edu
Newsgroups: sci.math
From: cyeomans@ms.uky.edu (Charles Yeomans)
Subject: Re: Fermat's Last Theorem
    <1992Apr9.081944.6101@cunixf.cc.columbia.edu>
Date: Thu, 9 Apr 1992 14:48:19 GMT
Organization: University Of Kentucky, Dept. of Math Sciences
X-Bytes: 

In article <1992Apr9.081944.6101@cunixf.cc.columbia.edu> gd1@cunixa.cc.columbia.edu (Gautam Dalmia) writes:
>For now, flame this:
>
>===========================================================================
>In high school I read number theory and realized the the beauty of
>mathematics: the  simple unanswered questions and the elusive, but
>simple, answers. Then, one day, I went to a library to look at
>journals/ big books and alas ... mathematicians had invented abstruse,
>ugly methods to attack these beautiful questions. At first I was
>saddened but then I looked up, and I laughed and said "God, what fools
>these mathematicians be".... and God and I have been laughing ever since! 

Perhaps they seem abstruse and ugly because you lack the ability
to appreciate the beauty of these methods.  As my art history
professor once said, there's no accounting for taste".

Charles Yeomans
cyeomans@ms.uky.edu
yeomans@austin.onu.edu

Newsgroups: sci.math