Comments for Involutions

Comment on My favorite word problem by vlorbik

vlorbik — Fri, 06 Jul 2007 18:10:40 +0000

then there’s the plane that takes 8 hours to fly from A to B
*against* the wind, but only 7 hours to fly back from B to A
*with* the wind. evidently the wind is blowing at a constant
rate for 15 hours over a stretch of thousands of miles.

what kind of drugs are these people *on*?
(& how can *i* get some?)

Comment on Introduction to Differentials by vlorbik

vlorbik — Fri, 06 Jul 2007 18:05:58 +0000

much clearer than in the textbooks!

if this seems like i’m damning with faint praise,
i suppose it might be because i’m not at all sure
that this should be part of introductory courses *at all* …

Comment on Concept classification via Google page counts by Coconuts

Coconuts — Sun, 03 Jun 2007 01:18:13 +0000

Interesting work! It reminds me a lot of Latent Semantic Analysis, which similarly calculates similarity between terms by how often they co-occur in documents. The algorithm that LSA uses is a little more complicated, and, I think, might address some of the weaknesses pointed out in the paper. I think it might be neat to try to combine the two approaches, maybe by using google to find a more "interesting" document set to feed to LSA.

Comment on Concept classification via Google page counts by Carnival of Mathematics IX « JD2718

Carnival of Mathematics IX « JD2718 — Sat, 02 Jun 2007 14:24:57 +0000

[...] attempts to Classify Concepts by search engine page Counts. [...]

Comment on Proof of Burnside’s Lemma using Multiorbits by involution

involution — Wed, 14 Mar 2007 13:25:12 +0000

Hi Andy! It turns out that two random permutations in S_n will generate all of S_n, with probability approaching 3/4 as n tends to infinity. Also, two random permutations in A_n will generate A_n, with probability approaching 1 as n tends to infinity.

Reference: Dixon, John D. The probability of generating the symmetric group. Mathematische Zeitschrift 110 (1969), No. 3, 199-205.
http://www.springerlink.com/content/r4×1444382133111/

Comment on Proof of Burnside’s Lemma using Multiorbits by Andy D

Andy D — Mon, 26 Feb 2007 05:30:12 +0000

Hi Involution! Thanks for the link… This is a nice proof of Burnside’s Lemma, thanks for sharing it.

I am not much of a group theorist… but have an occasional curiosity. The last problem I remember thinking about, pretty ineffectually, was,

If we choose k elements of the symmetric group S_n at random, what is the expected size of the subgroup generated by them?

Of course, we should expect exponential growth in k while k is small… but can we do better?

If you know of any refs (or have ideas), I’d love to hear about them… thanks!