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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
7
votes
2
answers
471
views
A quadratic form
Let $q$ be a power of 2. Let $P$ be the set of polynomials in
$F_q [x]$ of degree d or less.
Let $\mathbb{Z}$ be the ring of integers. For any $f \in P$, let $\psi(f)$ be the
number of distinct roo …
5
votes
1
answer
1k
views
Number of integral points inside a small sphere
Is there a good asymptotic estimation for the number of integral points
inside a $n$-sphere of a small radius ( less than $\sqrt{n}$)?
It looks like a problem which has been studied, however, I cannot …