## Science University Research Symposium (SURS)

#### Title

### Solving the Bubble Path Problem

#### Publication Date

2023

#### College

Sciences and Mathematics, College of

#### Department

Math and Computer Science, Department of

#### SURS Faculty Advisor

Dr. Adam Cartisano

#### Presentation Type

Oral Presentation

#### Abstract

Let M be a 4 x *n* binary matrix with exactly one non-zero entry per row. The Bubble Path Problem asks the probability *P(n)* for a given matrix of length *n* that a path can be made under certain conditions, passing through only entries of value 0 from the top to the bottom rows. In this presentation, we introduce the Bubble Path Problem and some interesting patterns present in the problem. We then discuss an initial combinatorial approach, a solution strategy that uses inductive reasoning and Markov chains, and potential future expansions.

#### Recommended Citation

Goskie, Maxwell, "Solving the Bubble Path Problem" (2023). *Science University Research Symposium (SURS)*. 93.

https://repository.belmont.edu/surs/93