Results 91 to 100 of about 920 (172)
Algebraic languages and polyominoes enumeration
, 1984 In this paper, the use of algebraic languages theory in solving an open problem in combinatorics is shown. By constructing a bijection between convex polyominoes and words of an algebraic language, and by solving the corresponding algebraic system, we ...
Viennot, Gérard, Delest, Marie-Pierre
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Asymptotic Analysis and Random Sampling of Digitally Convex Polyominoes [PDF]
, 2013 International audienceRecent work of Brlek \textit{et al.} gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to
A. Jacquot +7 more
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Polyominoes and graphs built from Fibonacci words
, 2022 16 pages, 8 figuresInternational audienceWe introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing
Ramírez, José Luis, Kirgizov, Sergey
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Discrete mathematics as a resource for developing scientific activity in the classroom. [PDF]
ZDM, 2022 Colipan X, Liendo A.
europepmc +1 more source
Tiling rectangles with holey polyominoes
, 2014 We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability.
Tristrom Cooke, Dmitry Kamenetsky
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Counting Polyominoes, Revisited
Abstract A polyomino is an edge-connected set of squares on the square lattice. In this paper, we improve Jensen's algorithm for counting polyominoes by considering bounding boxes on the square lattice rotated by 45o instead of on the regular unrotated lattice. This allows us to extend significantly the count of polyominoes from 56 to 70 terms.
Gill Barequet, Gil Ben-Shachar
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Generating Trees and Fibonacci Polyominoes
We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the number of ...
Ramírez, José L. +2 more
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The number of Z-convex polyominoes
, 2006 In this paper we consider a restricted class of polyominoes that we call Z-convex polyominoes. Z-convex polyominoes are polyominoes such that any two pairs of cells can be connected by a monotone path making at most two turns (like the letter Z).
Gilles Schaeffer +8 more
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Level and pseudo-Gorenstein path polyominoes
We classify path polyominoes which are level and pseudo-Gorenstein. Moreover, we compute all level and pseudo-Gorenstein simple thin polyominoes with rank less than or equal to 10.
Rinaldo, Giancarlo +2 more
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Reconstructing hv-convex multi-coloured polyominoes
, 2010 In this paper, we consider the problem of reconstructing polyominoes from information about the thickness in vertical and horizontal directions. We focus on the case where there are multiple disjoint polyominoes (of different colours) that are hv-convex,
Bains, Adam +3 more
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