4 papers
Characterizing -syndetic, -thick, and related notions of size using derived sets along ultrafilters
Shea D. Burns, Dennis Davenport, Shakuan Frankson +3
We characterize relative notions of syndetic and thick sets using, what we call, "derived" sets along ultrafilters. Manipulations of derived sets is a characteristic feature of alg…
Finding an Isomorphism between the Riordan Group and a Subgroup of the Double Riordan Group
Shakuan Frankson
The Riordan group is a set of infinite lower-triangular matrices defined by two generating functions, and . The elements of the group are called Riordan arrays, denoted by $…
The Relationship Between Pascal's Triangle and Random Walks
Tonia Bell, Shakuan Frankson, Nikita Sachdeva +1
Random walks are a series of up, down, and level steps that enumerate distinct paths from to , where is the semi-length of the path. We used these paths to anal…
Investigating First Returns: The Effect of Multicolored Vectors
Shakuan Frankson, Myka Terry
By definition, a first return is the immediate moment that a path, using vectors in the Cartesian plane, touches the -axis after leaving it previously from a given point; the in…