Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Banach Spaces On Infinitely Branching Trees, Annette B. Locke
Banach Spaces On Infinitely Branching Trees, Annette B. Locke
Electronic Theses and Dissertations
An example of a Banach space, X∞, with a nonseparable dual such that l1 does not imbed in X∞ is investigated. Not every weakly null sequence has a subsequence equivalent to the usual basis of c0, but c0 imbeds in many subspaces of X∞. The space l1 does imbed in X∞∗, the dual space of X∞, yet weakly converging sequences in X∞∗ need not converge in norm.
Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly
Permutation Patterns, Reduced Decompositions With Few Repetitions And The Bruhat Order, Daniel Alan Daly
Electronic Theses and Dissertations
This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including Stanley, Billey and Tenner. In particular, they studied pattern avoidance conditions on reduced decompositions with no repeated elements. This thesis classifies the pattern avoidance and containment conditions on reduced decompositions with one and two elements repeated. This classification is then used to obtain new enumeration results for pattern classes related to the reduced decompositions and introduces the technique of counting pattern classes via reduced …