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

1998/09/29 by Jonathan King, Jonathan L. King, King, Jonathan L.
Computer Science · Engineering · Mathematics · #05B45 #Architecture and Computational Design #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B45

paper · pdf · doi:10.48550/arxiv.math/9809176

18 pages, 3 figures. Will appear in the proceedings of the First International Conference on Semigroups & Algebraic Engineering, held in Aizu-Wakamatsu City, Japan, in March 1997

arxiv created 1998/09/29 · openalex publication_date 1998/09/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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