DOAJ Open Access 2011

Closed paths whose steps are roots of unity

Gilbert Labelle Annie Lacasse

Lihat Sumber DOI

Abstrak

We give explicit formulas for the number $U_n(N)$ of closed polygonal paths of length $N$ (starting from the origin) whose steps are $n^{\textrm{th}}$ roots of unity, as well as asymptotic expressions for these numbers when $N \rightarrow \infty$. We also prove that the sequences $(U_n(N))_{N \geq 0}$ are $P$-recursive for each fixed $n \geq 1$ and leave open the problem of determining the values of $N$ for which the $\textit{dual}$ sequences $(U_n(N))_{n \geq 1}$ are $P$-recursive.

Topik & Kata Kunci

Mathematics

Penulis (2)

Gilbert Labelle

Annie Lacasse

Format Sitasi

APA MLA BibTeX

Labelle, G., Lacasse, A. (2011). Closed paths whose steps are roots of unity. https://doi.org/10.46298/dmtcs.2937

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2937

Informasi Jurnal

Tahun Terbit: 2011
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2937
Akses: Open Access ✓