Bruce Fang

Researched under Professor Leo Goldmakher

• Worked with another student on average behavior of higher power residues; one paper in preparation

Researched under Professor Steven J. Miller

• Collaborated with a group of students to revise and extend results from SMALL REU 2015, one paper ready to submit
• Studied Ramsey-theoretic problems on large sets without 3-term geometric progressions in Hurwitz quaternion order

Researched under Professor Pamela E. Harris

• Worked with two other students in parking functions; one paper ready for submission
• Defined a new type of parking functions called vacillating parking functions
• Found a recursive formula for the enumeration of general vacillating parking functions
• Defined a nice subset of vacillating parking functions and derived an explicit formula for its enumeration

Researched under Professor Steven J. Miller

• Collaborated with a group of high school students on Zeckendorf Decomposition Problem; one paper published in Fibonacci Quarterly
• Generalized Zeckendorf Decomposition to 2-dimensional lattice and obtained the probability mass formula for the gap vectors between terms of legal decompositions