Comments for Portrait of the Mathematician

Comment on GILA 2: The probabilistic approach by blogs

blogs — Fri, 17 May 2013 10:28:44 +0000

Inform potential clients of the the huge benefits that
the goods can offer them. Get back, perhaps
the lowest firms are able to get available online for
and also be significant. They focus on all the parts which
are important for internet marketing.

Comment on The coupon collectors’ problem by the flex belt review

the flex belt review — Wed, 13 Feb 2013 04:54:38 +0000

The belt could be worn wherever so you can get a amazing function out
taking a cat nap or washing house.

Comment on GILA 2: The probabilistic approach by Blas

Blas — Wed, 16 Jan 2013 11:58:01 +0000

In the Theorem, when you say that “(In fact, we can take N=3)”, it is not true. We have A={1,2,4} in {1,2,3,4} or A={1,2,4,5} in {1,2,3,4,5} as counterexamples. I think that the right number would be N=5, if I am not wrong.
Also, I do not understand very well how the probabilistic proof of the Theorem ends. If a random subset of {1,…,n} of density >2/3 contains a random 3-AP with positive probability, I do not see how can we deduce that EVERY subset with that density contains one.
In any case, I agree with the Theorem; I can prove without probabilistic methods that given delta>2/3 we have an N such that every subset of {1,..,n} with n>N and at least delta·n elements contains three consecutive integers.
But if you could explain more clearly the probabilistic proof and how it guarantees the existence of N satisfying the Theorem, that would throw some light…
Many thanks.

Comment on Well, well, well. Look who’s come crawling back by Harrison

Harrison — Sun, 22 Jul 2012 22:40:10 +0000

Credit where credit’s due: I stole the tag from Scott Aaronson’s blog.

Comment on Well, well, well. Look who’s come crawling back by Rod Carvalho

Rod Carvalho — Sun, 22 Jul 2012 22:32:54 +0000

I love your “embarrassing myself” tag. Will adopt it!

Comment on The coupon collectors’ problem by abdelhak salim

abdelhak salim — Sat, 24 Mar 2012 23:04:35 +0000

abdelhak salim…

[...]The coupon collectors’ problem « Portrait of the Mathematician[...]…

Comment on I’m in love. What’s that song? by Afina Pallada

Afina Pallada — Fri, 29 Apr 2011 17:07:02 +0000

I am in love too

Comment on Full HAP tables for the second 1124 sequence by Tony Guilfoyle

Tony Guilfoyle — Sun, 03 Apr 2011 21:10:00 +0000

>(Probably someone specific discovered it, but I don’t know who.)

It was me. (Or rather my laptop.) Go to http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/ and search for 1124.

Comment on More on graphs and digraphs by colinwytan

colinwytan — Fri, 11 Jun 2010 14:02:57 +0000

I think a good question ask is what is the adjoint from Groupoids to Graphs to your “free groupoid” construction? If you take up to isomorphism, you don’t get much left. A skeletal groupoid forgets to a series of vertices.

What this really means is that the “free groupoid” construction doesn’t preserve the combinatorial information you want from your graph. However, it does very well preserve the connectedness information of your graph. (Which is reflected in its adjoint).

The other thing is that there is too low dimensions here. (in the sense of geometry or higher categories) There are only two kinds of 1-manifolds, circle of line. Graphs with at most 2 edges at each vertex, viewed as a 1-complex, realizes as a 1-manifold. That you speak of “number of vertices and edges” which determine the fundamental groupoid is your combinatorial way of putting this geometry.

Comment on The importance of choosing the right model by colinwytan

colinwytan — Fri, 11 Jun 2010 13:43:17 +0000

Harrison, where did you read about real computation? Is there published work on computability theory with real numbers instead of natural numbers? It seems that polymath2 would need some real computation.