Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

https://hal.inria.fr/hal-01215040
Contributor : Coordination Episciences Iam <>
Submitted on : Tuesday, October 13, 2015 - 3:05:25 PM
Last modification on : Friday, March 27, 2020 - 3:18:03 PM
Long-term archiving on: : Thursday, April 27, 2017 - 12:28:37 AM

File

dmAO0153.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01215040, version 1

Collections

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. ⟨hal-01215040⟩

Share

Metrics

Record views

129

Files downloads

490