Professional paper

Cyclic up-down words

Sela Fried ; Computer Science Department, Israel Academic College in Ramat Gan *

* Corresponding author.

Abstract

A word \(w_{1}w_{2}\cdots w _{n}\) of even length n is said to be cyclic up-down if \( w_{1}< w_{2}>w _{3}\cdots and w _{n}>w _{1}\). We find the generating function for the number of cyclic up-down words over {1, 2, . . . , k}, from which a closed-form formula is derived. We also construct a bijection with semi-magic labelings of certain graphs, called cycle-of-loops graphs.

Keywords

Chebyshev polynomial, cyclic up-down word, generating function, semi-magic labeling

Hrčak ID:

341424

URI

https://hrcak.srce.hr/341424

Publication date:

17.12.2025.

Visits: 347 *