# Publications

## Dimensions of Automorphism Group Schemes of Finite Level Truncation of F-Cyclic F-Crystals

Available at To appear in Transactions of the American Mathematical Society, 2019

In this paper, we develop a combinatorial formual to calculate the dimension of the automorphism group of F-cyclic F-crystal over an algebraically close dfield at some finite level. This is a joint work with Zeyu Ding.

## Finding a Unique Finding a Unique Solution to Radon-Kaczmarz Puzzles

Available at Pi Mu Epsilon Journal, 2018

In this paper, we determine the size of a Radon-Kaczmarz Puzzle so that it has a unique solution when give a fixed set of clues. This is a joint work with Steven Rossi.

## Minimal F-crystals and Isomorphism Numbers of Isosimple F-crystals

Available at Mathematische Nachrichten, 2017

In this paper, we generalize minimal p‐divisible groups to minimal F-crystals. Using minimal heights, we give an estimate of isomorphism number of isosimple F-crystals.

## Subtle Invariants of F-crystals

Available at Journal of Ramanujan Mathematical Society, 2014

In this paper, we prove Vasiu’s conjecture that the isomorphism number of an F-crystal is equal to its level torsion.