  A proof is sketched of the Polynomial Conjecture of the author (circulated as
preprint "Brick Tiling and Monotone Boolean Functions", available at the
http://www.math.ufl.edu/~squash/tilingstuff.html url) which says that the
family of minimal tilable-boxes grows polynomially with dimension. An important
ingredient of the argument is translating the problem from its
finite-dimensional geometric framework to the algebraic setting of an
infinite-dimensional lattice.
