Multiplicative generalised polynomial sequences

Abstract: Generalised polynomials are sequences constructed from polynomial sequences using the integer part function, addition, and multiplication. Determining whether a given sequence is a generalised polynomial is often a non-trivial task. In joint work with J. Byszewski and B. Adamczewski, we have discovered both surprising examples of such sequences and developed criteria to disprove that a given sequence is a generalised polynomial. More broadly, given a family of sequences, one can pose a classification problem: Which sequences in the family are generalized polynomials? In this talk, I will present a complete resolution of this problem for the family of multiplicative sequences, as well as partial results for (non-completely) multiplicative sequences.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)