College

Buchtel College of Arts and Sciences

Date of Last Revision

2021-05-11 19:22:37

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

partitionCreator.py (10 kB)
The associated Python3 program.

Heim Final Signature Page.pdf (223 kB)
Signature Page

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