Davidson Fellows - 2013 Fellow William Kuszmaul


William Kuszmaul

$10,000 Scholarship Recipient

Age: 17
Lexington, MA
Category: Mathematics
Project Title: “Equivalence Classes of Permutations Created Under Pattern-Replacement Relations”______ _______ ________ ____ _______


In English, certain words such as "soda" and "pop" are synonymous. A natural question to ask is how many really distinct meanings are there in the English language? In mathematics, a similar question is asked, except with permutations instead of English words, and with well-defined notions of equivalence corresponding with synonymousness.  This leads to the study of equivalence classes of permutations created under pattern replacement relations. 

William extended the systematic analysis of this question and developed new proof techniques that may help future researchers. His paper solves several open problems in the field of pattern replacement relations, in addition to continuing the systematic study of certain families of pattern replacement relations.  His work also contributed several new proof techniques that have been used to other related problems.  William hopes his work opens new directions for research in the area of pattern replacement relations, which has applications in both physics and abstract algebra and spectroscopy.

William is a rising senior at Lexington High School.  He hopes to be a professor of mathematics or computer science.  William was a 2011 and 2012 Siemens Competition Regional Finalist.  He was invited to the Canada/USA Mathcamp in 2012 and 2013, and won the silver medal at the National Latin Exam last year.  William enjoys Aikido and volunteered at the Boston Museum of Science.

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Click here to view the full listing of the 2013 Davidson Fellows. 
Click here to view William's press release.

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