Combinatorial Methods for Barcode Analysis

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.

Primes and Perfect Powers in the Catalan Triangle

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.