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 ����.

Volume

22

Published in

Annals of Combinatorics

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.

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