quotients of weighted projective spaces. We then show that the BHK mirrors provided in the example are birational.

[**Acknowledgments.**]{} The author would like to thank Charles Siegel, Ting Chen, Alberto García-Raboso, Antonella Grassi, and Tony Pantev for their enlightening conversations on the subject. He would like to give special thanks to his advisor, Ron Donagi, for the support, mentoring, conversations and introducing him to the Berglund-Hübsch literature. This work was done under the support of a National Science Foundation Graduate Research Fellowship.

Berglund-Hübsch-Krawitz Duality
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We start with a matrix $A$ with nonnegative integer entries $(a_{ij})_{i,j=0}^n$. Define a polynomial $$F_A = \sum_{i=0}^n \prod_{j=0}^n x_j^{a_{ij}}$$ and impose the following conditions:

1.  the matrix $A$ is invertible;

2.  the polynomial $F_A$ is quasihomogeneous, i.e., there exist positive integers $q_j, d$ so that $$\sum_{j=0}^n a_{ij} q_j  = d,$$ for all $i$; and

3.  the polynomial $F_A$ is a non-degenerate potential away from the origin, i.e., we are assuming that, when viewing $F_A$ as a polynomial in ${\mathbb{C}}^{n+1}$, $Z(F_A)$ has exactly one singular point (at the origin).

These conditions are restrictive. By Theorem 1 of [@KS], there is a classification of such polynomials. That is, $F_A$ can be written as a sum of invertible 