Other Mathematics Commons^™

Results On The Generalized Covering Radius Of Error Correcting Codes, Benjamin Langton

HMC Senior Theses

The recently proposed generalized covering radius is a fundamental property of error correcting codes. This quantity characterizes the trade off between time and space complexity of certain algorithms when a code is used in them. However, for the most part very little is known about the generalized covering radius. My thesis seeks to expand on this field in several ways. First, a new upper bound on this quantity is established and compared to previous bounds. Second, this bound is used to derive a new algorithm for finding codewords within the generalized covering radius of a given vector, and also to …

An Exploration Of Voting With Partial Orders, Mason Acevedo

HMC Senior Theses

In this thesis, we discuss existing ideas and voting systems in social choice theory. Specifically, we focus on the Kemeny rule and the Borda count. Then, we begin trying to understand generalizations of these voting systems in a setting where voters can submit partial rankings on their ballot, instead of complete rankings.

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …