Geneva Schlafly | Searcharxiv

arXiv2020

On Isomorphic K-rational Groups of Isogenous Elliptic Curves over Finite Fields

We show that two ordinary isogenous elliptic curves have isomorphic groups of rational points if they have the same $j$-invariant and we extend this result to certain isogenous supersingular elliptic curves, namely those with equal $j$-invariant of either 0 or 1728. Using a result by Heuberger and Mazzoli we establish a general case of this relationship within isogenous elliptic curves not necessarily having equal $j$-invariant.

math.NT↗

arXiv2019

Edge Disjoint Caterpillar Realizations

In this paper, we consider the edge disjoint caterpillar realizations of tree degree sequences. We give the necessary and sufficient conditions when two tree degree sequences have edge disjoint caterpillar realizations. We conjecture that an arbitrary number of tree degree sequences have edge disjoint realizations if every vertex is a leaf in at most one tree. We prove that the conjecture is true if the number of tree degree sequences is at most $4$. We also prove that the conjecture is true if $n \ge \max\{22k-11, 396\}$, where $n$ is the number of vertices and $k$ is the number of tree degree sequences.

math.CO↗