Seminario: "Fibonacci partitions, automata, and generalized spectral radiis" - Carlo Sanna

Séminaire TNGA

LMNO - Laboratoire de mathématiques Nicolas Oresme, November 21, 2025, 14:00

https://lmno.unicaen.fr/evenement/seminaire-tnga-trois-exposes-de-carlo-sanna-antonella-perucca-et-florian-luca/

Abstract. For each positive integer n, let r_F(n) be the number of ways to write n as a sum of distinct Fibonacci numbers, where the order of the summands does not matter. What is the average of r_F(n) ? More generally, what is the k-th moment of r_F(n) ? Chown, Jones, and Slattery answered these questions for k=1,2 via counting arguments and inequalities. In turns out that, thanks to ideas of Berstel and Shallit, these questions can be answered by employing automata theory and a result on the generalized spectral radius.