Results 41 to 50 of about 920 (172)
Combinatorics of non-ambiguous trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by Aval, Boussicault ...
Jean-Christophe Aval +3 more
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A $q,t-$analogue of Narayana numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study the statistics $\mathsf{area}$, $\mathsf{bounce}$ and $\mathsf{dinv}$ associated to polyominoes in a rectangular box $m$ times $n$. We show that the bi-statistics ($\mathsf{area}$,$\mathsf{bounce}$) and ($\mathsf{area}$,$\mathsf{dinv}$) give ...
Jean-Christophe Aval +4 more
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A New Algorithm Based on Colouring Arguments for Identifying Impossible Polyomino Tiling Problems
Algorithms, 2022 Checkerboard colouring arguments for proving that a given collection of polyominoes cannot tile a finite target region of the plane are well-known and typically applied on a case-by-case basis. In this article, we give a systematic mathematical treatment
Marcus R. Garvie, John Burkardt
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A Tiling-Theoretic Approach to Efficient Area Coverage in a Tetris-Inspired Floor Cleaning Robot
IEEE Access, 2018 Although numerous studies have focused on the development and application of polyomino tiling theories, research of this nature is typically limited to the graphics and gaming fields.
Prabakaran Veerajagadheswar +3 more
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A code for square permutations and convex permutominoes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and convex permutoninoes, a related subclass of ...
Enrica Duchi
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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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Interactions between Digital Geometry and Combinatorics on Words [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry. Motivated on the one hand by the well-known theory of Sturmian words which model conveniently discrete lines in the plane, and on ...
Srečko Brlek
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On the exact complexity of polyomino packing [PDF]
Theoretical Computer Science, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hans L. Bodlaender +1 more
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Decidability of multiset, set and numerically decipherable directed figure codes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Codes with various kinds of decipherability, weaker than the usual unique decipherability, have been studied since multiset decipherability was introduced in mid-1980s.
Włodzimierz Moczurad
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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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