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Trine faculty member’s article on number theory published

By Noah Swift
Communication ’22

Thomas MorrillA Trine University faculty member recently had an article published in the International Journal of Number Theory.

Thomas Morrill, Ph.D., assistant professor of mathematics, co-authored “Quasimodularity of the k-th Residual Cranks.” The article discusses number theory, covering two perspectives on the same problem: modularity and combinatorics.

Combinatorics, Morrill said, is the abstract study of counting. For example, the number four can be written five ways in terms of whole numbers:

  • 4 = 4
  • 4 = 3 + 1
  • 4 = 2 + 2
  • 4 = 2 + 1 + 1
  • 4 = 1 + 1 + 1 + 1

“Each of these solutions is called a partition,” they explained. (Morrill is non-binary.) “Mathematicians like me use statistics to study partitions; the crank is one of these statistics. It compares the number of times one appears in the partition against the larger numbers in the partition. The residual crank is our contribution to the field; it measures the parts of partitions according to whether they are divisible by a fixed number k.”

Morrill specializes in partitions and generating series in mathematics. They uncovered these functions in scratch work from their Ph.D. research. Co-author Aleksander Simonič is currently a Ph.D. student at the University of New South Wales – Canberra who shares an interest in modularity.

A preprint of the paper is available at