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seen Mar 20 '13 at 7:53

Mar
4
comment Colorings of a set
You, sir, are a genius. One minor problem: shouldn't it be |A1|<=4*3^n instead of just <? And is the rest of the solution like: 4*3^n = (4 choose 3)*3^n, therefore.....?
Feb
25
comment A Problem about friends and strangers using Ramsey's Theory
R(3,3) = 6, which is the number of that guy's friends. However, there are 8 persons in total. How can we safely ignore that other guy?
Feb
25
asked A Problem about friends and strangers using Ramsey's Theory
Feb
25
accepted Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
Feb
25
comment Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
Never mind, I have figured it out. Thanks! :)
Feb
25
comment Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
I don't see how you can always "remove edges of any perfect matching to get (d−1)-regular bipartite graph with (d−1) distinct perfect matchings." How? Is it possible that such removal cannot be done? Let's say we start removing one edge from each vertex from the side that has a perfect matching into the other side. What if 2 edges got removed connect with the same vertex on the other side and that vertex cannot maintain a d-1 degree???
Feb
25
revised Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
edited tags
Feb
25
comment Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
Thanks for fixing that.
Feb
25
revised Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
added 82 characters in body
Feb
25
asked Let G be a bipartite graph all of whose vertices have the same degree d. Show that there are at least d distinct perfect matchings in G
Dec
13
awarded  Commentator
Dec
13
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
Awesome, this makes perfect sense to me!
Dec
13
accepted Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
Dec
5
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
Also, is it true that we only have to do it in 3 parts? Why are we ignoring the line segments?
Dec
5
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
The residues at the 2 poles are 1/(2e^2) at x=-1 and e^2/2 at x=1. Clearly the part at the top part doesn't equal to 0. I guess.
Dec
5
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
@mrf It'll be great if you can walk us through this. This problem just does not make any sense to me.
Dec
5
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
@DonAntonio: Yup, I checked for like 10 times because it apparently does not converge... But it is what it is in the question.
Dec
5
comment Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour
Yup, I am pretty confused about why this question is asked this way too. I think the point is to ask what happens in each part of the contour and have everything cancelled out in the process of working it out. This is where my problem is too.. Just wondering if my guess of doing it in 6 parts is correct and how I work it our part by part....
Dec
5
accepted Questions regarding finite Blaschke product
Dec
5
asked Evaluate $ \ \int_{- \infty}^{\infty} \frac{x e^{2ix}}{x^2 - 1}\,dx \ $ using given contour