[arijun]

I stopped reading earlier, when they used superscript without explaining its meaning. Its clearly meant for someone with more domain expertise than me, with my hazy recollections of college math.

[Ar-Curunir]

That is just exponentiation, eg squaring. They’re just putting symbols instead of numbers there.

[arijun]

But then they say A + A <= A^2, wouldn’t that be false for a = 1?

[pfdietz]

In this context, A is a set, and A + A represents the set of all sums of pairs of elements drawn from A.

The paper doesn't use A^2, but rather |A|^2, which is ordinary squaring of an integer. It does use AA, which is the set of products of pairs of elements drawn from A.