4 problems

Propp's Laurent phenomenon conjecture. Every value $f_v(t)$ of the unbounded cube recurrence is a Laurent polynomial in ${\mathbf x}$.

Consider a superimposition formed by combining the edges of two groves on different sets of initial conditions, allowing translations, so that the result is a multiset of edges. Th…

Let $x_{i,j,k}$ denote the initial variables in a polynomial generated by the cube recurrence. Propp's exponent-bound conjecture. In each term of any polynomial generated by the cu…

Let $f_{i,j,k}$ be the Laurent polynomials generated by the cube recurrence from general initial conditions, with coefficients viewed after the recurrence has been expanded as Laur…