Work

The Schur polynomials in all primitive nth roots of unity

Year: 2025

Type: article

Abstract: We show that the Schur polynomials in all primitive n th roots of unity are 1, 0, or −1, if n has at most two distinct odd prime factors. This result can be regarded as a generalization of properties of the coefficients of the cyclotomic polynomial and its multiplicative inverse. The key to the proof is the concept of a unimodular system of vectors. Namely, this result can be reduced to the unimodularity of the tensor product of two maximal circuits (here we call a vector system a maximal circuit, if it can be expressed as B ∪ { − ∑ B } with some basis B ).

Source: Journal of Combinatorial Theory Series A

DOI: 10.1016/j.jcta.2025.106107

Authors: Masaki Hidaka, Minoru Itoh

Institution: Kagoshima University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,210

Funder: Japan Society for the Promotion of Science