Murdoch University Research Repository

Welcome to the Murdoch University Research Repository

The Murdoch University Research Repository is an open access digital collection of research
created by Murdoch University staff, researchers and postgraduate students.

Learn more

Rich, Sturmian, and trapezoidal words

De Luca, A., Glen, A.ORCID: 0000-0002-9434-3412 and Zamboni, L. (2008) Rich, Sturmian, and trapezoidal words. Theoretical Computer Science, 407 (1-3). pp. 569-573.

PDF - Authors' Version
Download (96kB)
Free to read:
*No subscription required


In this paper we explore various interconnections between rich words, Sturmian words, and trapezoidal words. Rich words, first introduced by the second and third authors together with J. Justin and S. Widmer, constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors. Every finite Sturmian word is rich, but not conversely. Trapezoidal words were first introduced by the first author in studying the behavior of the subword complexity of finite Sturmian words. Unfortunately this property does not characterize finite Sturmian words. In this note we show that the only trapezoidal palindromes are Sturmian. More generally we show that Sturmian palindromes can be characterized either in terms of their subword complexity (the trapezoidal property) or in terms of their palindromic complexity. We also obtain a similar characterization of rich palindromes in terms of a relation between palindromic complexity and subword complexity.

Item Type: Journal Article
Publisher: Elsevier BV
Copyright: 2008 Elsevier B.V.
Item Control Page Item Control Page


Downloads per month over past year