Title
Jacobi–Trudi determinants over finite field
Department/School
Mathematics
Date
7-16-2018
Document Type
Article
Abstract
In this paper, we work toward answering the following question: given a uniformly random algebra homomorphism from the ring of symmetric functions over ℤ to a finite field ����, what is the probability that the Schur function ���� maps to zero? We show that this probability is always at least 1/q and is asymptotically 1/q. Moreover, we give a complete classification of all shapes that can achieve probability 1/q. In addition, we identify certain families of shapes for which the events that the corresponding Schur functions are sent to zero are independent. We also look into the probability that Schur functions are mapped to nonzero values in ����.
Published in
Annals of Combinatorics
COinS
Citation/Other Information
Anzis, B., Chen, S., Gao, Y., Kim, J., Li, Z., & Patrias, R. (2018). Jacobi-Trudi determinants over finite fields. Annals of Combinatorics. 22: 447-489. https://doi.org/10.1007/s00026-018-0399-8.