October 11, 2021
A Trine University mathematics professor had an article published in the September
2021 edition of the journal Research in Number Theory.
Thomas Morrill, Ph.D., assistant professor in the Department of Mathematics and Physics, co-authored a paper regarding combinatorics, the mathematical discipline of abstract counting. The article, "A Stanley-Elder Theorem on Cranks and Frobenius symbols," demonstrates an unexpected relationship between the so-called cranks of integer partitions, and the Frobenius symbols that represent those same partitions.
The aforementioned topics provide different perspectives on the same fundamental problem, according to Morrill.
"There are only so many ways to write a whole number using addition only -- three, or two-and-one, or one-one-one. The crank is a measurement of how many ones appear in the solution," Morrill added. "The Frobenius symbol is different. It's a much more geometrical approach. No one expected these things to agree, ever!"
Morrill met co-authors George Andrews and Manosij Dastidar over the summer via email. Notably, Andrews was involved in the initial discovery of partition cranks in the 1980s. The group plans to extend their results in a follow-up paper in the near future.
Research in Number Theory is an international, peer-reviewed journal covering the mathematical disciplines of number theory and arithmetic geometry.
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