New interface

# Closed paths whose steps are roots of unity

Abstract : 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.
Keywords :
Document type :
Conference papers
Domain :
Complete list of metadata

Cited literature [5 references]

https://hal.inria.fr/hal-01215040
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, October 13, 2015 - 3:05:25 PM
Last modification on : Thursday, October 13, 2022 - 8:27:39 AM
Long-term archiving on: : Thursday, April 27, 2017 - 12:28:37 AM

### File

dmAO0153.pdf
Publisher files allowed on an open archive

### Citation

Gilbert Labelle, Annie Lacasse. Closed paths whose steps are roots of unity. FPSAC: Formal Power Series and Algebraic Combinatorics, 2011, Reykjavik, Iceland. pp.599-610, ⟨10.46298/dmtcs.2937⟩. ⟨hal-01215040⟩

Record views