A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings

Details A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings

1998-09-29

arxiv.org/abs/math/9809176v1

Mathematics

Combinatorics

18 pages, 3 figures. Will appear in the proceedings of the First International Conference on Semigroups & Algebraic Engineerin

Scientific paper

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.

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