Comments on: Additive combinatorics

By: Jarek Kuben

Jarek Kuben — Sun, 17 Mar 2013 01:28:31 +0000

In the proof of Theorem 9.2, page 331, 15th line, should be t_{n-1}^{d_{n-1}} instead of t_{n-1}^{d_{n}-1}.

[Added, thanks - T.]

By: Small doubling in groups « What’s new

Small doubling in groups « What’s new — Fri, 01 Feb 2013 18:19:55 +0000

[...] much detail the proof techniques used in these results (although the abelian case is discussed in this book of mine with Vu, and the nonabelian case discussed in this more recent book of mine), but instead focuses on the [...]

By: Rafael Tesoro Carretero

Rafael Tesoro Carretero — Tue, 18 Dec 2012 10:59:11 +0000

I found the erratas list very useful, thanks for this! It seems to me another minor one may be the following. In the middle of page 264 there should be E instead of G, and the first pair should be (a,b) instead of (a',b'): |\{ (a,b) \in A \times B : (a,b'),(a',b'),(a',b) \in E \}| \ge \frac{|A||B|}{2^{12}K^5}. [Corrected, thanks - T.]

By: Yogesh Anbalagan

Yogesh Anbalagan — Thu, 15 Nov 2012 00:45:12 +0000

p. 315 In the proof of theorem 8.14 … the points (b+c, ac) with C ___ … C should be element of A ? Is that a typo?

[Yes; see the errata list for the revised edition. -T.]

By: ablmff

ablmff — Mon, 05 Nov 2012 14:07:31 +0000

Sorry, should be \|h + A\| [Erratum added, thanks - T.]

By: ablmff

ablmff — Mon, 05 Nov 2012 14:06:01 +0000

I think in Ex 4.3.2, \|T^h A\| should be \|h A\|.

By: ablmff

ablmff — Sun, 14 Oct 2012 20:58:23 +0000

I think there might be a bit ambiguity in exercise 2.5.7. It says: G \subset A \times A is such that every element of A is connected via G to at least K^{-1}|A| elements of |A|. Here, does the A in "every element of A" refer to the first A in "A \times A", or to both of them? [To both; I'll add an erratum to clarify this. -T]

By: Terence Tao

Terence Tao — Wed, 10 Oct 2012 02:53:34 +0000

One should be able to construct an example for all sufficiently large N (of course, the claim is trivial for very small N, e.g. N=1).

By: ablmff

ablmff — Tue, 09 Oct 2012 15:35:12 +0000

In 2.3.23, we are asked to give an example with certain properties, but do we need to give an example which works for all possible N, or can we choose a particular N?

By: ablmff

ablmff — Thu, 04 Oct 2012 14:32:15 +0000

Hi, for 2.2.6, isn't it easy to prove the bound \sqrt{ 2 \sigma[A] |A| } ? We are confused why 2 should be outside the square root. [Yes, you're right; this was actually correct in the first edition, but was mistakenly revised in the second edition. I'll add a new erratum to reflect this. -T]