-
To appear in Memoirs of the American Mathematical Society.
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions.
-
National Science Foundation research grant
This project aims to improve the proof-writing abilities of undergraduate students by training an innovative artificial intelligence model to provide feedback on student proofs to support both college students in proof-oriented mathematics courses and the post-secondary faculty who are teaching them.
-
The Permutation Pattern Avoidance Library (PermPAL) is a database of algorithmically-derived theorems about permutation classes. These results are produced by the Combinatorial Exploration framework.
-
Rutgers Experimental Mathematics Seminar (March 10, 2022)
Combinatorial Exploration is a framework that unifies the often ad-hoc methods used in enumerative combinatorics. In this talk we will explain how Combinatorial Exploration works, how it can be automated, and how it is applied to the study of pattern-avoiding permutations to prove new results and reprove dozens of old ones. We will also discuss the new web database PermPAL that catalogs these results.
-
Submitted.
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function enumerating GSAWs on a half-infinite strip of finite height is rational. We also compute generating functions for GSAWs under two probabilistic models and perform Monte Carlo simulations to estimate their expected length and displacement. Finally, we prove that the generating functions for Greek key tours on a half-infinite strip of fixed height are also rational, allowing us to resolve several conjectures.
-
Published in Enumerative Combinatorics and Applications.
We derive the algebraic generating function for inversion sequences avoiding the patterns 201 and
210 by describing a set of succession rules, converting them to a system of generating function equations with
one catalytic variable, and then solving the system with kernel method techniques
