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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 …
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  • 503
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 …
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  • 503