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Algebraic Structures on Sets of Partitions
Madeline L. Dawsey, Megan du Preez, Rachel Van Surksum
Motivated by Robert Schneider's trailblazing work toward developing a unifying algebraic theory of integer partitions, we explore various binary operations on partitions to identif…
Non-standard binary representations and the Stern sequence
Katie Anders, Madeline Locus Dawsey, Rajat Gupta +1
We show that the number of short binary signed-digit representations of an integer is equal to the -th term in the Stern sequence. Various proofs are provided, including dir…
Bijections, generalizations, and other properties of sequentially congruent partitions
Ezekiel Cochran, Madeline Locus Dawsey, Emma Harrell +1
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and…
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…