Tiling rectangles with polyominoes

Golomb, Solomon W.
March 1996
Mathematical Intelligencer;Spring96, Vol. 18 Issue 2, p38
Academic Journal
Presents a study on subjects of tiling, polyominoes and decidability, areas in which fundamental contributions were made by Raphael Robinson. Problems in maths when a speech was made by German mathematician David Hilbert; Information on the Incompleteness Theorem; Areas in tiling which cause mathematical problems.


Related Articles

  • Undecidability of compass logic. Marx, M; Marx, Maarten; Reynolds, M; Reynolds, Mark // Journal of Logic & Computation;Dec99, Vol. 9 Issue 6 

    Presents a tiling technique that can be used to give proofs of undecidability of various two-dimensional modal and temporal logics. Uses of compass logic; Variations and applications of logics; Undecidability of validity in temporal logics using the domino or tiling technique; Axiomatization of...

  • Tilings*. Ardila, Federico; Stanley, Richard // Mathematical Intelligencer;Dec2010, Vol. 32 Issue 4, p32 

    The article offers information about mathematical puzzle and the ways to solve it. It informs about tilings in the puzzles which raises various questions regarding number of tilings, relation among different tilings and symmetry in tilings. It takes into consideration polyaminoes puzzles by...

  • Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids. Kirsten, D.; Richomme, G. // Theory of Computing Systems;May/Jun2001, Vol. 34 Issue 3, p193 

    In the last decade, research on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the importance of the finite power property to achieve partial solutions to this problem. We prove that the star problem is decidable in some trace...

  • Some probability logics with new types of probability operators. Ognjanovic, Z; Raskovic, M // Journal of Logic & Computation;Apr99, Vol. 9 Issue 2, p181 

    Introduces new types of probability operators of the form Q(sub F), where F is a recursive rational subset of [0,1]. Axiomatic systems for a number of probability logics augmented with the Q(sub F)-operators; Decidability of the presented logics.

  • On Algorithmic Problems for Joins of Pseudovarieties. Steinberg, B. // Semigroup Forum;2001, Vol. 62 Issue 1, p1 

    This paper considers the algorithmic problems of decidability (of membership), decidability of pointlikes and idempotent pointlikes, and hyperdecidability for joins of pseudovarieties of semigroups. In particular, we show that if \pv V\subseteq \pv J has a decidable word problem for its...

  • Comparing expressibility of normed BPA and normed BPP processes. Cerná, Ivana; Křetínsky, Mojmír; Kučera, Antonín // Acta Informatica;1999, Vol. 36 Issue 3, p233 

    Summary. We present an exact characterization of those transition systems which can be equivalently (up to bisimilarity) defined by the syntax of normed BPA[sub tau] and normed BPP[sub tau] processes. We give such a characterization for the subclasses of normed BPA and normed BPP processes as...

  • On the Tiling System Recognizability of Various Classes of Convex Polyominoes. De Carli, F.; Frosini, A.; Rinaldi, S.; Vuillon, L. // Annals of Combinatorics;2009, Vol. 13 Issue 2, p169 

    We consider some problems concerning two relevant classes of two-dimensional languages, i.e., the tiling recognizable languages, and the local languages, recently introduced by Giammarresi and Restivo and already extensively studied. We show that various classes of convex and column-convex...

  • Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry. Fukuda, Hiroshi; Kanomata, Chiaki; Mutoh, Nobuaki; Nakamura, Gisaku; Schattschneider, Doris // Symmetry (20738994);Dec2011, Vol. 3 Issue 4, p828 

    We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There...

  • A Method to Generate Polyominoes and Polyiamonds for Tilings with Rotational Symmetry. Fukuda, Hiroshi; Mutoh, Nobuaki; Nakamura, Gisaku; Schattschneider, Doris // Graphs & Combinatorics;Jun2007 Supplement 1, Vol. 23, p259 

    We show a simple method to generate polyominoes and polyiamonds that produce isohedral tilings with p3, p4 or p6 rotational symmetry by using n line segments between lattice points on a regular hexagonal, square and triangular lattice, respectively. We exhibit all possible tiles generated by...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics