Proof is in the Pattern

Mathematics student’s summer research led to development of new theorems.

Alanna Pellicane writing equations on a clear board. Alanna Pellicane writing equations on a clear board.

From Isaac Newton to Albert Einstein to Katherine Johnson, you might think all mathematical theories have already been discovered. In truth, new math is discovered every day — in part by young scholars like SUNY Brockport mathematics major Alanna Pellicane.

Over the summer, Pellicane participated in the Summer Undergraduate Research Program (SURP), living and working on campus alongside her mentor, Dr. Rebecca Smith. Her research opportunity was funded by the LoBracco Family Research Scholars Award, which covered her room and board expenses while she lived on campus and conducted research over the summer.


Pellicane working in the Math Tutoring Center.

“I loved it so much, it was an amazing experience,” Pellicane said. “I’m reapplying for the undergraduate research program this summer to hopefully build one more good foundation on what I’m doing, and then hopefully I’ll apply to an REU (Research Experience for Undergraduates) in the future.”

Pellicane’s work involved looking at “words” and developing theorems to avoid certain sequences. In mathematics, a word is a sequence of symbols, often represented by numbers.

“Say I want to avoid the pattern 01. The word 0100 has that pattern in it, so that’s a bad word,” Pellicane explained. “So, we want to find all the good words that avoid that pattern and create a theorem to avoid those bad words.”

Practical applications for theorems like the one Pellicane and Smith developed can range from data analysis to statistical biology.

Going to the conference really has opened up so many opportunities for me.
Alanna Pellicane

“Different patterns might be interesting for different applications,” Smith said. “A lot of it is related to data structures with computer science, and that’s kind of the foundational problems there.”

Pellicane had the opportunity to present her research on pattern avoidance within words at the 2026 Joint Mathematics Meeting — a national conference held annually in Washington, D.C.

“Going to the conference really has opened up so many opportunities for me, I don’t even know what to do with my summers anymore,” Pellicane said. “I was just presented all these opportunities that I have to build my network.”

As a sophomore, she’d definitely be among the youngest people there…and she really held her own.
Dr. Rebecca Smith

Pellicane presented at the student poster session alongside student researchers from across the country.

“I just love sharing my research with people and them asking questions and showing that they genuinely care about it and are interested. It’s so cool,” Pellicane said.

Pellicane, currently a sophomore, is part of a small group of students who get the opportunity to share their research at a national conference early in their college careers.

“As a sophomore, she’d definitely be among the youngest people there…and she really held her own,” Smith said. “She got great feedback from the judges.”

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