## Search found 15 matches

Mon Oct 04, 2010 1:10 pm UTC
Forum: Mathematics
Topic: Simple question; Polynomials modulo n
Replies: 2
Views: 595

### Re: Simple question; Polynomials modulo n

Ah, I see... Thanks.
Mon Oct 04, 2010 10:34 am UTC
Forum: Mathematics
Topic: Simple question; Polynomials modulo n
Replies: 2
Views: 595

### Simple question; Polynomials modulo n

Hi there. This should be a fairly simple question, but I was just suddenly caught up in doubt, and I couldn't find a reasonable explanation. If I'm looking at a polynomial ring R[X] where R is any ring. Are the "degrees" (or the powers, if you will) then (integer-) elements from R, always ...
Tue Sep 21, 2010 12:45 pm UTC
Forum: Mathematics
Topic: Which is it? (straight line or circle through a portal?)
Replies: 33
Views: 5041

### Re: Which is it?

So T and I are homotopy equivalent, and in fact are both H.E. to a point. A and R are also homotopy equivalent. In fact, all uppercase letters are H.E. to either A,B, or C. Not all lowercase letters are, though... can you figure out which ones aren't? Well, clearly 'i' and 'j' wouldn't be, but all ...
Fri Sep 17, 2010 11:22 am UTC
Forum: Mathematics
Topic: Which is it? (straight line or circle through a portal?)
Replies: 33
Views: 5041

### Re: Which is it?

Ah, so 'T' would be homotopic to 'I', since we can continuously deform one into the other, but not homeomorphic, since, if you remove the point connecting the vertical to the horizontal line in 'T' you get three components, whereas 'I' can only be divided into two separate components. Am I right? Or...
Tue Sep 14, 2010 1:51 pm UTC
Forum: Mathematics
Topic: 0 is not an even number
Replies: 34
Views: 4167

### Re: 0 is not an even number

Mike_Bson wrote:What's next, something representing less than nothing?

Signatured...
Tue Sep 14, 2010 1:31 pm UTC
Forum: Mathematics
Topic: Which is it? (straight line or circle through a portal?)
Replies: 33
Views: 5041

### Re: Which is it?

Homeomorphic != homotopic. The rope between the portals is very much homeomorphic to the circle: as someone mentioned above, it is pretty clearly an interval with its two endpoints identified. When you're building topology from scratch, this is often taken as the definition of a circle, as it's sup...
Mon Sep 13, 2010 8:33 pm UTC
Forum: Mathematics
Topic: Which is it? (straight line or circle through a portal?)
Replies: 33
Views: 5041

### Re: Which is it?

Why is that so?

(I'm not questioning the truth in this, I'm sincerely interested in a broader explanation )
Thu Apr 08, 2010 10:32 am UTC
Forum: Mathematics
Topic: Commuting permutations
Replies: 5
Views: 4185

### Commuting permutations

Okay, so I'm teaching myself some algebra here, and I just need to cement some of the relations. We have that disjoint permutations commute, a permutation commutes with itself, and therefore all powers of itself, and the identity, of course, commutes with everything. So to find the set of all permut...
Wed Apr 07, 2010 4:37 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Re: Power of permutation-cycle

Ah, so if I'd have to do p^3, how would you calculate the new cycle type?

EDIT: Forget this...
Wed Apr 07, 2010 4:16 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Re: Power of permutation-cycle

Oh, and another thing...

Wouldn't any p^k, where k is greater than 4 give the same result?
Wed Apr 07, 2010 4:14 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Re: Power of permutation-cycle

(Alternatively since you've factored 1864 as 233*8, you can use the fact that a cycle to a coprime power is still the same cycle, so the 233 does nothing and you can find the cycle type of p^8 instead. This will agree with the cycle type of p^4 as long as neither has any even lenght cycles (hence t...
Wed Apr 07, 2010 3:53 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Re: Power of permutation-cycle

Okay, but what I don't quite understand, is how to do this. I assume that to find the order, I have to know the "new" cycle type. Is there any "fast" way to do this? What I did was: Original cycle type 4^1*5^1*6^1. A 4-cycle squared becomes 2 2-cycles, and a 2-cycle squared becom...
Wed Apr 07, 2010 3:17 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Re: Power of permutation-cycle

mike-l wrote:If the order of p is 60, what is p^120? p^180? p^1800? p^1860?

They would all be the identity, of course, so in this case p^1864 = p^4, right? So we have to find the order and cycle type of p^4?
Wed Apr 07, 2010 2:54 pm UTC
Forum: Mathematics
Topic: Power of permutation-cycle
Replies: 9
Views: 3282

### Power of permutation-cycle

HI all... A pretty basic algebra question, that I need some help with, just to clarify things. Assume you are given a permutation, p, in the symmetric group S_15. All you know about the permutation is the cycle type, which is (4^1)(5^1)(6^1), eg. 1 cycle of length 4, 1 cycle of length 5 and 1 cycle ...
Fri Dec 11, 2009 9:17 am UTC