Published in Arxiv Pre-Print, under review, 2022
We study a new partial order on the space of barcodes closely related to the permutahedron. The resulting poset has connections to continuous metrics on barcodes such as the bottleneck and Wasserstein distances.
Published in Arxiv Pre-Print, scheduled to appear in American Mathematical Monthly with J. De Loera, D. Oliveros, and A. Torres, 2022
We study the intersections of time dependent events using an original random interval graph model.
Published in Journal of Integer Sequences with N. Benjamin, G. Fickes, E. Fiorini, E. Jovinelly, and T.W.H. Wong, 2019
The Catalan triangle is an infinite lower-triangular matrix that generalizes the Catalan numbers. The entries of the Catalan triangle, denoted by \(c_{n,k}\), count the number of shortest lattice paths from \((0, 0)\) to \((n, k)\) that do not go above the main diagonal. This paper studies the occurrence of primes and perfect powers in the Catalan triangle.
Published in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (Conference Paper) with S. Han and J. Yu., 2018
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other.