Yes. The definition of mathematical fields is very fuzzy, but there are many questions which seem to belong to both “Number Theory” and “Combinatorics”. For example: in how many ways can a positive integer be represented as a sum of four integer sq…

]]>On p239, exercise 5.5.17: I don’t think this example works. The problem is that the midpoints of the quadrilateral , , , themselves form a parallelogram, and this rules out any non-standard Freiman homomorphisms to .

Replacing the generic quadrilateral with a generic pentagon in should fix it, I think, giving a universal ambient group of .

(Also, I think there is a typo

on the penultimate line: the first “2” should be a “4”.)

*[Correction added, thanks – T.]*

On p241, proof of Lemma 5.45, last line of the first displayed equation: I think

should read

as an estimate on the binomial coefficient.

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

p. 285: Corollary 5.25 should be Lemma 5.25.

*[Correction added, thanks – T.]*

on page 281, last paragraph it says “we can reduce further to the case that $Z$ is odd”, which should probably read “$|Z|$ is odd” or “the order of $Z$ is odd”?

PS: I do not know if it is actually useful to report such minor typos?

*[Correction added, thanks -T.]*

On page 294, after the very first proof (of 7.20), it says “however one can lower dimension its by increasing”, probably instead of “lower its dimension by increasing”.

*[Correction added, thanks – T.]*

*[Correction added, thanks – T.]*

in the final lines of the proof of Freiman’s 3k-3 Theorem (page 208) it appears that the inequality is used reversed, and I can’t see how the relative errata above can fix this. Am I wrong?

*[Gah, the previous erratum was not applied correctly. I’ve now supplied a revised erratum in the second errata list. -T.]*