The first meeting of the Carolina Mathematics Seminar took place at the University of South Carolina Sumter, Sumter, SC. This is a list of our speakers, titles and abstracts.
Alexandru Gabriel Atim (Benedict College)
Title: On balanced property of words over finite alphabet.
Abstract: Sturmian words are infinite words over a binary alphabet that has exactly n+1 factors of length n for every n. Morse-Heldun Theorem states that this equivalent to the set of all balanced aperiodic words. In this talk we will generalize the balanced property on words and then we will classify all words having this property.
Rebecca Hillman (USC Sumter)
Title: On Products of Fibonacci Numbers and Their Recurrence Relations.
Abstract: Various products of Fibonacci numbers and their generalizations are investigated and recurrence relations for these products are obtained.
Jason Holt (USC Lancaster)
Title: Estimates for the negative eigenvalues for a Random Schroedinger Operator with a decaying perturbation.
Abstract: We will discuss a one dimensional random Schoedinger Operator with a decaying perturbation. We will give sufficient condition for the existence of finitely many negative eigenvalues. The model is closely related to the one dimensional motion of a quantum particle in a crystal lattice.
Leandro Junes (USC Sumter)
Title: What is an oriented matroid?
Abstract: An oriented matroid is a combinatorial structure inspired by a hyperplane arrangement. In this talk I will give an informal definition of oriented matroid from a Geometric view point. I will also discuss its interrelations with Graph Theory, Linear Programming and Topology.
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