20th Annual Student Research Conference
Mathematics and Computer Science
Affinely Self-Generating Sets and Morphisms
Adam C. Gouge
Dr. David Garth, Faculty Mentor
Kimberling defined a self-generating set S of integers as follows. Assume 1 is a member of S, and if x is in S, then 2x and 4x-1 are in S. We study similar self-generating sets of integers whose generating functions come from a class of affine functions for which the coefficients of x are powers of a fixed base. We prove that for any positive integer m, the resulting sequence, reduced modulo m, is the image of an infinite word that is the fixed point of a morphism over a finite alphabet. We also prove that the resulting characteristic sequence of S is the image of the fixed point of a morphism of constant length, and is therefore automatic.
Keywords: mathematics, self-generating sets, sequences, affine functions, morphisms, modulo arithmetic, missing blocks, Fibonacci numbers
Topic(s):Mathematics
Presentation Type: Poster
Session: 5-1
Location: OP Lobby
Time: 4:15 pm