Rarely do they use Additive Combinatorics. Sources suggest it could be a good a resource as any. They just don’t.

]]>Today is 17th july 1975

Happy birthday to you,I am expecting your new breakthrough works. ]]>

To see it, first notice that your usage of in (2) is implying this definition of Big-O notation (see also here):

if and only if there exist constants and such that for all .

Using this notation, we have for , then for *, and then for all .*

*[The final use of (2) is needed to control for negative . -T.]*

paper was on the editors table for almost 10 months, but the experts on the field wouldn`t referee it. ]]>

But isn’t the sum of quasimorphism and a constant simply a quasimorphism?

Let be a quasimorphism and let for all and for a constant .

Now .

By triangle-inequality we have

.

Now because is a translation invariant metric, the right side is equal to .

*[This is technically true, but only if one is willing to lose control of the quasimorphism constants; I have reworded this paragraph to address this point. -T]*

*[Corrected, thanks – T.]*

*[Corrected, thanks – T.]*

We have with and the height of . I'm even straining to find the definition of "height" here… if as reduced fractions, then we have .

This is a set of measure zero, but maybe I can cover each rational point with a small interval? If I rotate this circle by 45 degrees, none of this set overlaps with itself, so this circle is definitely not rotationally symmetric.

]]>*[Corrected, thanks – T.]*