Counting Schreier-Type Sets (Hung Chu)

Remote: this project is scheduled to begin on 6/08/2026 and run for 6 weeks, finishing on 7/17/2026.

Project Description

A finite set F of natural numbers is called a Schreier set if the minimum element of F is at least the cardinality of F. For example, {4,5,11} is a Schreier set because its minimum element is 4, while its cardinality is 3. However, the set {2,4,7} is not a Schreier set because its minimum element is 2, which is smaller than its cardinality, 3. Various connections between Schreier sets and interesting integer sequences have been discovered. A notable result, due to A. Bird, states that the number of Schreier sets whose maximum element is n is equal to the n-th Fibonacci number. In this project, we will study different Schreier-type conditions, count the sets that satisfy these conditions, and explore the integer sequences that arise from this counting.

Prerequisites

Students should have completed MATH 225 – Bridges to Advanced Mathematics. Completion of an additional proof-based course is strongly preferred.

Special Comments

Project Information (subject to change)

Estimated Start Date: 6/08/2026

Estimated End Date: 7/17/2026

Estimated Project Duration: 6 weeks

Maximum Number of Students Sought: 2

Research Location: Remote

Travel Required? No (If “yes”: )

Contact Information: Hung Chu (email: hchu@wlu.edu)