Solving the Bubble Path Problem
Sciences and Mathematics, College of
Math and Computer Science, Department of
SURS Faculty Advisor
Dr. Adam Cartisano
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.
Goskie, Maxwell, "Solving the Bubble Path Problem" (2023). Science University Research Symposium (SURS). 93.