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On Tilings By Ribbon Tetrominoes
 J. Combin. Theory, Ser. A
, 1999
"... Introduction A ribbon polyomino is a polyomino which has at most one square (i; j) in every diagonal i \Gamma j = c. A tetromino is a polyomino with four squares. Up to translations there are exactly 8 different ribbon tetrominoes, which we denote by 1 ; : : : ; 8 as in Fig. 1. Let T = f 1 ; : : ..."
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Cited by 7 (3 self)
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; : : : ; 8 g. 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = Fig. 1 Now let \Gamma be a simply connected region (a finite connected set of squares), and let be a tiling of \Gamma by ribbon tetrominoes. This means that \Gamma is covered 1 without intersection by parallel translations of ribbon tetrominoes.
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping generalpurpose computation to graphics hardware. We begin with the technical motivations that underlie generalpurpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping generalpurpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in generalpurpose application development on graphics hardware.
Tilings of rectangles with Ttetrominoes
 Theor. Comp. Sci
, 2003
"... We prove that any two tilings of a rectangular region by Ttetrominoes are connected by moves involving only 2 and 4 tiles. We also show that the number of such tilings is an evaluation of the Tutte polynomial. The results are extended to a more general class of regions. 1 ..."
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We prove that any two tilings of a rectangular region by Ttetrominoes are connected by moves involving only 2 and 4 tiles. We also show that the number of such tilings is an evaluation of the Tutte polynomial. The results are extended to a more general class of regions. 1
Tetromino tilings and the Tutte polynomial
, 2008
"... We consider tiling rectangles of size 4m × 4n by Tshaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polyno ..."
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Cited by 1 (0 self)
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We consider tiling rectangles of size 4m × 4n by Tshaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte
Ribbon tilings and multidimensional height function
 TRANS. AMER. MATH. SOC
, 2001
"... We fix n and say a square in the twodimensional grid indexed by (x, y) has color c if x + y ≡ c (mod n). A ribbon tile of ordern is a connected polyomino containing exactly one square of each color. We show that the set of ordern ribbon tilings of a simply connected region R is in onetoone co ..."
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Cited by 6 (1 self)
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We fix n and say a square in the twodimensional grid indexed by (x, y) has color c if x + y ≡ c (mod n). A ribbon tile of ordern is a connected polyomino containing exactly one square of each color. We show that the set of ordern ribbon tilings of a simply connected region R is in one
Ribbon Tile Invariants from Signed Area
 Journal of Combinatorial Theory Ser. A
, 2000
"... Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were rst introduced in [P], where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works by associat ..."
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Cited by 5 (3 self)
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Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were rst introduced in [P], where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works
Ribbon tile invariants
 Trans. Amer. Math. Soc
, 1997
"... Abstract. Let T be a finite set of tiles, and B a set of regions Γ tileable by T. We introduce a tile counting group G(T, B) as a group of all linear relations for the number of times each tile τ ∈ T can occur in a tiling of a region Γ ∈B. We compute the tile counting group for a large set of ribbon ..."
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Cited by 7 (2 self)
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of ribbon tiles, alsoknown as rim hooks, in a context of representation theory of the symmetric group. The tile counting group is presented by its set of generators, which consists of certain new tile invariants. In a special case these invariants generalize the ConwayLagarias invariant for tromino tilings
A Survey of Shape Analysis Techniques
 Pattern Recognition
, 1998
"... This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems. ..."
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Cited by 261 (2 self)
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This paper provides a review of shape analysis methods. Shape analysis methods play an important role in systems for object recognition, matching, registration, and analysis. Researchin shape analysis has been motivated, in part, by studies of human visual form perception systems.
Results 1  10
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