Picture child's feet next to pens, pencils and paper

Open Access research that is helping to improve educational outcomes for children

Strathprints makes available scholarly Open Access content by researchers in the School of Education, including those researching educational and social practices in curricular subjects. Research in this area seeks to understand the complex influences that increase curricula capacity and engagement by studying how curriculum practices relate to cultural, intellectual and social practices in and out of schools and nurseries.

Research at the School of Education also spans a number of other areas, including inclusive pedagogy, philosophy of education, health and wellbeing within health-related aspects of education (e.g. physical education and sport pedagogy, autism and technology, counselling education, and pedagogies for mental and emotional health), languages education, and other areas.

Explore Open Access education research. 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.