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Self-conjugate -core partitions and applications
Madeline Locus Dawsey, Benjamin Sharp
Partition theory abounds with bijections between different types of partitions. One of the most famous partition bijections maps each self-conjugate partition of a positive integer…
Derivatives and Integrals of Polynomials Associated with Integer Partitions
Madeline Locus Dawsey, Tyler Russell, Dannie Urban
Integer partitions express the different ways that a positive integer may be written as a sum of positive integers. Here we explore the analytic properties of a new polynomial $f_λ…
Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures
Madeline Locus Dawsey, Dermot McCarthy
Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their general…