Picture of sea vessel plough through rough maritime conditions

Innovations in marine technology, pioneered through Open Access research...

Strathprints makes available scholarly Open Access content by researchers in the Department of Naval Architecture, Ocean & Marine Engineering based within the Faculty of Engineering.

Research here explores the potential of marine renewables, such as offshore wind, current and wave energy devices to promote the delivery of diverse energy sources. Expertise in offshore hydrodynamics in offshore structures also informs innovations within the oil and gas industries. But as a world-leading centre of marine technology, the Department is recognised as the leading authority in all areas related to maritime safety, such as resilience engineering, collision avoidance and risk-based ship design. Techniques to support sustainability vessel life cycle management is a key research focus.

Explore the Open Access research of the Department of Naval Architecture, Ocean & Marine Engineering. Or explore all of Strathclyde's Open Access research...

On unavoidable sets of word patterns

Burstein, Alexander and Kitaev, Sergey (2005) On unavoidable sets of word patterns. SIAM Journal on Discrete Mathematics, 19 (2). pp. 371-381. ISSN 1095-7146

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern overlaps introduced in this paper, which is a subgraph of the de Bruijn graph and which we prove to be Hamiltonian. In other cases we reduce a problem under consideration to known facts on unavoidable sets of words. We also give a relation between our problem and intensively studied universal cycles, and prove there exists a universal cycle for word patterns of any length over any alphabet.