College
Buchtel College of Arts and Sciences
Date of Last Revision
2023-05-04 10:40:57
Major
Computer Science
Honors Course
3450 498-002
Number of Credits
2
Degree Name
Bachelor of Science
Date of Expected Graduation
Spring 2021
Abstract
The combinatorial theory of partitions has a number of applications including the representation theory of the symmetric group. A particularly important result counts the number of standard Young tableau of a given partition in terms of the hook lengths of the partition. In this paper we explore the analog of the hook length formula for plane partitions, the three-dimensional analog of ordinary partitions. We show that equality does not always hold but we conjecture that a certain inequality holds. Using a computer program, we verify this conjectured inequality for all 1982 plane partitions up to n = 11.
Research Sponsor
James P. Cossey
First Reader
Stefan A. Forcey
Second Reader
Zhone-Hui Duan
Honors Faculty Advisor
Curtis Clemons
Recommended Citation
Heim, Nicholas, "Exploring Plane Partitions" (2021). Williams Honors College, Honors Research Projects. 1413.
https://ideaexchange.uakron.edu/honors_research_projects/1413
The associated Python3 program.
Heim Final Signature Page.pdf (223 kB)
Signature Page