Freedom Math Dance

A blog about math (mainly), computer tricks (sometimes) and jazz music.

Thursday, November 19, 2020

Simple cases for non-simplicity

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A subgroup $H$ of a group $G$ is said to be normal if one has $gH=Hg$ for every $g\in G$. The French terminology is that $H$ be distingu...
Wednesday, May 13, 2020

Using texexec to modify a PDF file (from the shell)

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We all regularly have to modify a PDF file, either taking a part of it. The texexec program which is shipped with ConTeXt allows to do most...
Sunday, April 12, 2020

Some proofs of the quadratic reciprocity law

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Gauss's quadratic reciprocity law is a mysterious relation between prime numbers. If $p$ and $q$ are distinct prime numbers, it shows t...
2 comments :
Wednesday, February 12, 2020

Dynamics of Hecke correspondences

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This morning, Sebastián Herrero, Ricardo Menares and Juan Rivera-Letelier released a preprint on the arXiv entitled “ p-Adic distribution of...
Friday, December 27, 2019

Behaviour of conjugacy by reduction modulo integers

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Let $A$ and $B\in\mathrm{M}_n(\mathbf Z)$ be two square matrices with integer coefficients. Assume that they are conjugate by $\mathrm{GL}_n...
2 comments :
Tuesday, July 2, 2019

Irreducibility of cyclotomic polynomials

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For every integer $n\geq 1$, the $n$th cyclotomic polynomial $\Phi_n$ is the monic polynomial whose complex roots are the primitive $n$th ro...
3 comments :
Sunday, May 19, 2019

Designs, Skolem sequences, and partitions of integers

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Recently, my father offered me the first volume of a graphic novel by Jean-François Kierzkowski and Marek called La suite de Skolem — Skole...
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Antoine Chambert-Loir
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