Papers and Preprints

Concordances of linear combinations of T(2,q) torus knots to L-space knots (with Thomas Sachen)

To appear in Journal of Knot Theory and its Ramifications 

Continuing the work of Allen and Livingston, we work to further determine when a linear combination of torus knots is concordant to an L-space knot. This work was conducted at the 2020 Georgia Tech REU under supervision of Dr. JungHwan Park

Tantalizing properties of subsequences of the Fibonacci sequence modulo 10 (with aBa Mbirika and Miko Scott)

To appear in Rocky Mountain Journal of Mathematics

We explore properties of subsequences of a particular type of the Fibonacci sequence modulo 10. In particular, we examine when these sequences themselves follow a Fibonacci recurrence relation and when we recover the original modulo 10 sequence.

GCD of sums of k consecutive Fibonacci, Lucas and generalized Fibonacci numbers (with aBa Mbirika)

Published in Journal of Integer Sequences

By providing two vastly different, yet equivalent formulas involving a simple GCD and Pisano periods, we explicitly provide the GCD of sums of k consecutive Fibonacci and Lucas numbers. We also place restrictions on the GCD of sums of k consecutive generalized Fibonacci numbers in general. 

The C-complex clasp number of links (with Jonah Amundsen, Eric Anderson and Christopher Davis)

Published in Rocky Mountain Journal of Mathematics

For two and three component links, we establish the minimal number of clasps that they must have. In the two component case, we find that this is almost always the link's linking number. For three component links, we provide a lower bound by interpreting Milnor's triple linking number as the perimeter of a polyomino with fixed area.