 Our first main result shows that there is a polynomial-time computable, unique partially-ordered set of diagonal flips such that there is a bijection between valid linear-orderings of this set and minimum diagonal flip paths between two lattice triangulations .
<clarity>  Our first main result shows that there is a polynomial-time computable, unique partially-ordered set of diagonal flips such that there is a bijection between valid linear-orderings of this set and minimum diagonal flip paths between two lattice triangulations .
 Our first main result shows that there is a unique, partially-ordered set of diagonal flips such that there is a bijection between valid linear-orderings of this set and minimum diagonal flip paths between two lattice triangulations .