The second meeting of the Carolina Mathematics Seminar took place at the University of South Carolina Lancaster, Lancaster, SC. This is a list of our speakers, titles and abstracts.
Andrew Yingst (USC Lancaster)
Title: Partition Polynomials And Their Uses.
Abstract: If a coin has probability x of coming up heads, and E is a set of possible outcomes of finitely many tosses of this coin, then the probability of event E is a polynomial in x, referred to as a partition polynomial. We define and characterize these polynomials, and discuss some questions of dynamics on Cantor space that this characterization can be used to answer.
Leandro Junes (USC Sumter)
Title: From Hyperplanes to Oriented Matroid Programs.
Abstract: I will discuss the generalization of the simplex algorithm in Oriented Matroids. This will lead to an important class of Oriented Matroids called Euclidean Oriented Matroids.
Rigoberto Florez (USC Sumter)
Title: Some topics in harmonic matroids.
Abstract: A matroid is a combinatorial generalization of the linear independence concept. There are no linear relations, only dependent and independent sets. Many geometric properties extend to matroids. The harmonic conjugation extends from projective geometry to matroids. In this talk I am going to discuss some results in harmonic matroids.
Alexandru Gabriel Atim (Benedict College)
Title: On balanced property of words over finite alphabet (part II).
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.
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