Friday, October 13, 2023

A combinatorial proof of the Newton identities

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Let $T_1,\dots,T_n$ be indeterminates. For all $m\geq0$, denote by $S_m$ the $m$th elementary symmetric polynomial , given by \[ S_m = \sum...
Friday, August 4, 2023

On soccer balls

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This is a swift adaptation of a thread on Mastodon written after having read the beginning of Mara Goyet's column in yesterday's ed...
Thursday, July 6, 2023

Electrostatics and rationality of power series

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I would like to tell here a story that runs over some 150 years of mathematics, around the following question: given a power series $\sum a_...
Friday, February 17, 2023

Associated prime ideals

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$\gdef\ann{\mathop{\mathrm{ann}}} \gdef\Ass{\mathop{\mathrm{Ass}}}\gdef\Spec{\mathop{\mathrm{Spec}}}$ I would like to go back to a quite del...
Sunday, January 1, 2023

The Klein group, the centralizer of a permutation, and its relation with the alternating group

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The following reflexion came out of my irrepressible need to understand why the 3 double transpositions in $\mathfrak S_4$, together with th...
2 comments :
Monday, December 12, 2022

Multiplicative square roots

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I will just discuss briefly the first section of a paper by William Waterhouse (2012), “ Square Root as a Homomorphism ” ( American Mat...
Tuesday, November 1, 2022

#Mathober2022

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Sophia Wood (@fractalkitty) had the good idea to set up a #Mathober project: for each day of october, she proposes you to react to one word ...