Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Statistics and Probability

PDF

Macalester College

Series

2016

Articles 1 - 3 of 3

Full-Text Articles in Physical Sciences and Mathematics

Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway May 2016

Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway

Mathematics, Statistics, and Computer Science Honors Projects

In this thesis we develop a new method for constructing binary preference orders for given interdependent structures, called characters. We introduce the preference space, which is a vector space of preference vectors. The preference vectors correspond to binary preference orders. We show that the hyperoctahedral group, Z2 o Sn, describes the symmetries of binary preferences orders and then define an action of Z2 o Sn on our preference vectors. We find a natural basis for a preference space. These basis vectors are indexed by subsets of proposals. We show that when completely separable binary preference vectors are decomposed using this …


Bases For Mckay Centralizer Algebras, Lucas Gagnon May 2016

Bases For Mckay Centralizer Algebras, Lucas Gagnon

Mathematics, Statistics, and Computer Science Honors Projects

The finite subgroups of the special unitary group SU2 have been classified to be isomorphic to one of the following groups: cyclic, binary dihedral, binary tetrahedral, binary octahedral, and binary icosahedral, of order n, 4n, 24, 48, and 120, respectively. Associated to each group is a representation graph, which by the McKay correspondence is a Dynkin diagram of type Aˆ n−1, Dˆ n+2, Eˆ 6, Eˆ 7, or Eˆ 8. The centralizer algebra Zk(G) = EndG(V ⊗k ) is the algebra of transformations that commute with G acting on the k-fold tensor product of the defining representation V = C …


Blossom: A Language Built To Grow, Jeffrey Lyman Apr 2016

Blossom: A Language Built To Grow, Jeffrey Lyman

Mathematics, Statistics, and Computer Science Honors Projects

No abstract provided.