Nikolaus Conference 2021

Speaker: Balthazar Charles (Paris)

Title: Cartan Matrices of Finite Monoids and Fixed Point Counting


N. ThiƩry gave in 2012 a formula for computing the Cartan matrix of a finite monoid in terms of its character table and of the character of its regular representation.

We present an algorithmic implementation of this formula, with a particular focus on the algorithmic challenges of counting fixed points under a "conjugacy" action in a monoid.

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