Speaker
Gessica Alecci
(Politecnico di Torino, Italy)
Description
In 2020, Sagan and Tirrell introduced Lucas atoms, which are irreducible factors of Lucas polynomials. Their main goal was to investigate when certain combinatorial rational functions are actually polynomials. In a joint work with Miska, Murru, and Romeo, we present Lucas atoms in a more natural way than the original definition, providing straightforward proofs of their main properties. Moreover, we fully characterize the p-adic valuations of Lucas atoms for any prime p, thereby answering a question left open by Sagan and Tirrell. Finally, we show that the sequence of Lucas atoms is not holonomic, in contrast to the Lucas sequence, which satisfies a linear recurrence of order two.
