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plethysm

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John Baez

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Jun 29, 2010, 10:00:06 AM6/29/10
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What's the origin of the mathematical term "plethysm"?
I hear that someone suggested this term to Littlewood, but
who? And why? And what's the etymology?


tc...@lsa.umich.edu

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Jun 29, 2010, 11:30:01 AM6/29/10
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In article <i0cu96$m9c$1...@news.acm.uiuc.edu>,

According to the OED, a "plethysmograph" is "an instrument for recording
and measuring variation in the volume of a part of the body, or of the
whole body, esp. as caused by changes in blood pressure."
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences

WM

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Jun 29, 2010, 11:30:01 AM6/29/10
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On 29 Jun., 16:00, b...@math.removethis.ucr.andthis.edu (John Baez)
wrote:

> What's the origin of the mathematical term "plethysm"?  
> I hear that someone suggested this term to Littlewood, but
> who?  And why?  And what's the etymology?


Plethysmos means increase, multiplication (Greek). It is also used in
medicine and psychlogy for enlargement, increase.

Regards, WM

irvanellis

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Jun 30, 2010, 9:30:05 AM6/30/10
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On the question of the meaning and origin of plethysm:

> What's the origin of the mathematical term "plethysm"? I hear that someone
> suggested this term to Littlewood, but who? And why? And what's the
> etymology?


I believe that the term "plethysm" was introduced in:
MR0010594 (6,41c) Littlewood, D. E. Invariant theory, tensors and
group
characters.
Philos. Trans. Roy. Soc. London. Ser. A. 239, (1944). 305--365

It was suggested to Littlewood by M. L. Clark after the Greek word
plethysmos, for a third type of Schur function


$\pi\lambda\eta\theta\nu\sigma\mu o\zeta$ for "multiplication".


And the function was introduced in Littlewood's "Polynomial
Concomitants and Invariant Matrices", J. London Math. Soc. 11 (1936),
49-55.


Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info

John Baez

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Jun 30, 2010, 3:00:05 PM6/30/10
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Thanks, everyone!

I used some of your information to enhance the nLab entry on
plethysm:

http://ncatlab.org/nlab/show/plethysm

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