EAPSI: Analyzing Patterns in Permutations

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Permutations are a mathematical model that can be used to represent series of data like those found in computer algorithms and stock market trends. By carefully studying the frequency of various patterns in permutations, one can find a greater understanding of the data set itself. This project will investigate a special class of permutations that originates via the field of sorting machines in computer science. The research will be conducted with Professor Anthony Guttmann at the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems at the University of Melbourne.The researcher will apply the techniques originally developed by Guttmann for the study of phase transitions and critical phenomena in mathematical physics to the field of permutation patterns. The main goal of this project is to classify the asymptotic nature of a number of specific permutation classes that are conjectured to behave unlike any permutation class studied before. Furthermore, the researcher will utilize the computational resources of Guttmann to search for other permutation classes that may exhibit the same strange properties.This NSF EAPSI award supports the research of a U.S. graduate student and is funded in collaboration with the Australian Academy of Science.