Degree Growth of Holonomic Polynomial Sequences and Applications

05.04.2024 11:30 - 12:30

Shaoshi Chen (Academy of Mathematics and Systems Sciences (AMSS), Chinese Academy of Sciences (CAS), Beijing, China)

A sequence P_n(x) of polynomials in x is holonomic (P-recursive) if it satisfies a linear recurrence with polynomial coefficients in x and n. Many polynomial sequences from combinatorics, representation theory and number theory  are shown to be holonomic. It is natural and fundamental to study the degree growth of
holonomic polynomial sequences.  We will present a classification of the degree growth of such sequences and show two applications related to combinatorial identities  and exponential sums over finite fields respectively. This is a joint work with Jason P. Bell, Daqing Wan, Rong-Hua Wang and Hang Yin.

M. Schlosser
SR03, 1.OG, OMP1