Discrete Mathematics and Combinatorics Commons^™

Preferential Arrangement Containment In Strict Superpatterns, Martha Louise Liendo

Electronic Theses and Dissertations

Most results on pattern containment deal more directly with pattern avoidance, or the enumeration and characterization of strings which avoid a given set of patterns. Little research has been conducted regarding the word size required for a word to contain all patterns of a given set of patterns. The set of patterns for which containment is sought in this thesis is the set of preferential arrangements of a given length. The term preferential arrangement denotes strings of characters in which repeated characters are allowed, but not necessary. Cardinalities for sets of all preferential arrangements of given lengths and alphabet sizes …