The Schur polynomials in all primitive $n$th roots of unity
| Autor: | Hidaka, Masaki, Itoh, Minoru |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 notion of a unimodular system of vectors. Namely, this result is reduced in turn to four propositions on the unimodularity of vector systems, and the last proposition is proved by using graph theory. Comment: 12 pages; minor revision; title has been changed |
| Databáze: | arXiv |
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