Results 11 to 20 of about 920 (172)
Number of Spinal-Convex Polyominoes
Journal of Kufa for Mathematics and Computer, 2020 In his paper we describe a restricted class of polyominoes called spinal-convex polyominoes. Spinal-convex polyominoes created by two columns such that column 1 (respectively, column2) with at most two set columns sequence of adjacent ominoes and column ...
Mustafa A. Sabri, Eman F. Mohomme
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Counting Polyominoes on Twisted Cylinders [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We improve the lower bounds on Klarner's constant, which describes the exponential growth rate of the number of polyominoes (connected subsets of grid squares) with a given number of squares.
Gill Barequet +3 more
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A polyominoes-permutations injection and tree-like convex polyominoes
Journal of Combinatorial Theory, Series A, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gadi Aleksandrowicz +2 more
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Helly Numbers of Polyominoes [PDF]
Graphs and Combinatorics, 2012 We define the Helly number of a polyomino $P$ as the smallest number $h$ such that the $h$-Helly property holds for the family of symmetric and translated copies of $P$ on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist any polyomino with Helly number 3, (iii) there ...
Jean Cardinal +3 more
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Parallelogram Polyominoes and Corners
Journal of Symbolic Computation, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delest, Maylis +2 more
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On the Generation of 2-Polyominoes [PDF]
, 2018 The class of 2-polyominoes contains all polyominoes P such that for any integer i, the first i columns of P consist of at most 2 polyominoes. We provide a decomposition that allows us to exploit suitable discrete dynamical systems to define an algorithm for generating all 2-polyominoes of area n in constant amortized time and space O(n).
Enrico Formenti, Paolo Massazza
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Grammar-Based Evolution of Polyominoes [PDF]
Languages that describe two-dimensional (2-D) structures have emerged as powerful tools in various fields, encompassing pattern recognition and image processing, as well as modeling physical and chemical phenomena. One kind of two-dimensional structures is given by labeled polyominoes, i.e., geometric shapes composed of connected unit squares ...
Jessica Mégane +3 more
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The sandpile model, polyominoes, and a $q,t$-Narayana polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We give a polyomino characterisation of recurrent configurations of the sandpile model on the complete bipartite graph $K_{m,n}$ in which one designated vertex is the sink.
Mark Dukes, Yvan Le Borgne
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Algorithms, 2022 The general problem of tiling finite regions of the plane with polyominoes is NP-complete, and so the associated computational geometry problem rapidly becomes intractable for large instances.
Marcus R. Garvie, John Burkardt
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