Student NamePranav Chinmay
Faculty Mentor NameMiklós Bóna
CollegeCollege of Liberal Arts and Science
Research InterestsCombinatorics, algebra, number theory
Academic AwardsAnderson Scholar with Highest Distinction, Phi Beta Kappa Inductee Spring 2018, President's Honor Roll Fall 2016-Fall 2018
Hobbies and InterestsReading, racquet sports, chess, writing

Research Project

Enumerating stack-sortable permutations

The study of permutations of a finite list of objects yields rich and complex mathematics. One particularly young and fascinating area is stack-sorting and its interplay with pattern avoidance. A permutation of length n is said to be stack-sortable if passing it through a “stack” returns the identity permutation, 123…n. It can be shown that a permutation is stack-sortable if and only if it avoids the pattern 231, that is, it is impossible to pick three numbers (not necessarily consecutive) such that the smallest one is last, the largest one is in the middle, and the one in-between is first. For example, the permutation 1324 avoids the pattern 231, and hence it is stack sortable. This concept can be generalised to ask questions about t-stack sortable permutations, where the given permutation is passed through the stack t times. Beyond t=2, very little is known, and there are several open questions, which I hope to understand and hopefully answer.