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Consider the determinant: $$\Delta:= \left|\begin{array}{cccc} A_{j_1} & A_{k_1} & A_{j_1}A_{k_1} & 1 \\ A_{j_2} & A_{k_2} & A_{j_2}A_{k_2} & 1 \\ A_{j_3 } & A_{k_3 } &...

Let $n,H$ two fixed positive integers. Let $P\in\mathbb{Z}[X]$ a monic integral polynomial of height $H$ and degree $n$ taken uniformly at random (i.e. each of the $n$ free coefficients of $P$ is ...

The Perron-Frobenius theorem says that the largest eigenvalue of a positive real matrix (all entries positive) is real. Moreover, that eigenvalue has a positive eigenvector, and it is the only ...

The Cohen-Lenstra measure on the set of abelian p-groups assigns $\mathbb{P}(G) = \prod_{i \geq 1} \left( 1 - \frac{1}{p^i}\right) \cdot |\mathrm{Aut}(G)|^{-1} $. Apparently, this is equivalent to ...