Results 1 to 10 of about 2,994 (170)
The number of directed $k$-convex polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners.
Adrien Boussicault +2 more
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The number of $k$-parallelogram polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 A convex polyomino is $k$-$\textit{convex}$ if every pair of its cells can be connected by means of a $\textit{monotone path}$, internal to the polyomino, and having at most $k$ changes of direction.
Daniela Battaglino +3 more
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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 perimeter enumeration of column-convex polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 Combinatorics
Svjetlan Feretić
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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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Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations [PDF]
Entropy, 2018 We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs.
Hector Zenil +2 more
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Maximal increasing sequences in fillings of almost-moon polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino thatdo not contain a northeast chain of a fixed size depends only on the set of column lengths of the polyomino.
Svetlana Poznanović, Catherine H. Yan
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Hilbert series of parallelogram polyominoes [PDF]
Research in the Mathematical Sciences, 2022 AbstractWe present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed on the polyomino. By using a computational approach, we prove that the above conjecture holds for all simple polyominoes up to rank 11. In addition, we prove that the
Ayesha Asloob Qureshı +2 more
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Simple polyominoes are prime [PDF]
Journal of Commutative Algebra, 2017 In this paper we show that polyomino ideal of a simple polyomino coincides with the toric ideal of a weakly chordal bipartite graph and hence it has a quadratic Gr bner basis with respect to a suitable monomial order.
Ayesha Asloob Qureshı +2 more
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A Bijection for Directed-Convex Polyominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we consider two classes of lattice paths on the plane which use \textitnorth, \textiteast, \textitsouth,and \textitwest unitary steps, beginningand ending at (0,0).We enumerate them according to the number ofsteps by means of bijective ...
Alberto Del Lungo +3 more
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