Timeline for What is the theory of polynomials?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2012 at 14:55 | vote | accept | Jacques Carette | ||
| Aug 28, 2011 at 13:08 | comment | added | André Henriques | The word πληθυσμός means "population" in modern greek. The word for "multiplication is" πολλαπλασιασμός el.wikipedia.org/wiki/Πολλαπλασιασμός. | |
| Aug 25, 2011 at 18:49 | comment | added | Andrew Stacey | Yay for Tall-Wraith monoids! Incidentally, I've seen James Borger around here from time to time as well. | |
| Aug 25, 2011 at 18:15 | comment | added | Todd Trimble | @Jacques: I'm glad this seems to be in the neighborhood of what you were looking for (as some of the comments show, there is a variety of possible responses). Although complex, one could say the language of plethories is well-suited to express the incredible richness of algebraic structure borne by polynomial algebras (cf. $\Lambda$, the representation ring of the symmetric groups, and the manifold ways it arises in mathematics). | |
| Aug 25, 2011 at 17:10 | comment | added | Jacques Carette | @Todd: after having read the various links, I now see that 'plethory' is quite likely what I have been looking for. And much thanks for the link to Tall-Wraith monoids, as that pre-emptively answers a follow-up question I would have had! | |
| Aug 25, 2011 at 17:01 | comment | added | Jacques Carette | This is definitely an answer to my question. I can't help but think that a plethory requires an awful lot of structure just to get to polynomials! Do I really want the 'algebra of plethories' (i.e. a nice axiomatization of these, preferably in a not-too powerful logic), or the 'algebra of birings' (ditto)? Thanks for the links, I am reading all that now. Definitely relevant. | |
| Aug 25, 2011 at 17:00 | comment | added | Dan Petersen | The related term plethys in Greek means ‘a big number’ or ‘a throng’, and this in turn comes from the Greek verb plethein, which means ‘to be full’, ‘to increase’, ‘to fill’, etc. | |
| Aug 25, 2011 at 17:00 | comment | added | Dan Petersen | The word comes from "plethysm", which has been around in representation theory and invariant theory since forever. nLab says, quoting Richard Stanley, that the term was introduced in D. E. Littlewood, Invariant theory, tensors and group characters (1944) and that the term ‘plethysm’ was suggested to Littlewood by M. L. Clark after the Greek word plethysmos, or πληθυσμός, which means ‘multiplication’ in modern Greek (though apparently the meaning goes back to ancient Greek)... | |
| Aug 25, 2011 at 16:35 | comment | added | Qfwfq | (As a side question, I'm tempted to ask... what's so "plethoric" about plethories? Are they called like that because "there's a plethora of structure around"?) | |
| Aug 25, 2011 at 15:08 | history | answered | Todd Trimble | CC BY-SA 3.0 |