Cyclic up-down words

University of Zagreb University Computing Centre (SRCE) 2026 Open access

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Authors: Fried, Sela
Cited by: 0

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.

Fields of Study & Subjects

semigroups and automata theory Advanced Combinatorial Mathematics Advanced Graph Theory Research

Publication details

Journal / source
University of Zagreb University Computing Centre (SRCE)
Publication date
1 January 2026
Language
EN