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10 votes
3 answers
1k views

What's the number of solutions of the quadratic equation $x_1^2+\dots+x_m^2=0$ over finite ring $\mathbb{Z}/p^n$?

I want to calculate the number of solutions to the quadratic equation $$x_1^2+\dots+x_m^2=0$$ where $m$ is odd (a given number) and $x_i\in\mathbb{Z}/p^n$ for a given prime number $p$ and a given ...
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8 votes
1 answer
422 views

p-adic versions of log concavity for graphs (or matroids)

It was recently shown using techniques inspired by algebraic geometry (by Huh and Adiprasito-Huh-Katz) that the chromatic polynomial of a graph (or matroid) has coefficients that satisfy log-concavity....
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