Results 61 to 70 of about 1,340 (226)
Maximal 0-1-fillings of moon polyominoes with restricted chain lengths and rc-graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We show that maximal 0-1-fillings of moon polynomials, with restricted chain lengths, can be identified with certain rc-graphs, also known as pipe dreams.
Martin Rubey
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Generalized triangulations, pipe dreams, and simplicial spheres [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We exhibit a canonical connection between maximal $(0,1)$-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation.
Luis Serrano, Christian Stump
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Packing problems on generalised regular grid: Levels of abstraction using integer linear programming
Graphical Models, 2023 Packing a designated set of shapes on a regular grid is an important class of operations research problems that has been intensively studied for more than six decades. Representing a d-dimensional discrete grid as Zd, we formalise the generalised regular
Hao Hua, Benjamin Dillenburger
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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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Applied Sciences, 2018 Whilst Polyomino tiling theory has been extensively studied as a branch of research in mathematics, its application has been largely confined to multimedia, graphics and gaming domains.
Veerajagadheswar Prabakaran +4 more
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The combinatorics of Motzkin polyominoes
Discrete Applied MathematicsA word $w=w_1\cdots w_n$ over the set of positive integers is a Motzkin word whenever $w_1=\texttt{1}$, $1\leq w_k\leq w_{k-1}+1$, and $w_{k-1}\neq w_{k}$ for $k=2, \dots, n$. It can be associated to a $n$-column Motzkin polyomino whose $i$-th column contains $w_i$ cells, and all columns are bottom-justified.
Baril, Jean-Luc +3 more
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Signed polyomino tilings by n-in-line polyominoes and Gröbner bases
Publications de l'Institut Mathematique, 2016 Conway and Lagarias observed that a triangular region T(m) in a hexagonal lattice admits a signed tiling by three-in-line polyominoes (tribones) if and only if m 2 {9d?1, 9d}d2N. We apply the theory of Gr?bner bases over integers to show that T(m) admits a signed tiling by n-in-line polyominoes (n-bones) if and only if m 2 {dn2 ? 1, dn2}d2N.
Dizdarevic M. +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 Gröbner basis with respect to a suitable monomial order.
Qureshi, Ayesha Asloob +2 more
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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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Tiling Robotics: A New Paradigm of Shape‐Morphing Reconfigurable Robots
Advanced Intelligent Systems, Volume 7, Issue 9, September 2025.Tiling robotics is a novel paradigm of shape‐morphing reconfigurable robots, defining them as polyform‐inspired machines capable of transforming between at least two polymorphic shapes. Various reconfiguration‐enabling and locomotion mechanisms of tiling robots are comparatively analyzed, with the electromechanical developments, along with a proposed ...
S. M. Bhagya P. Samarakoon +2 more
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