Binary Pictures with Excluded Patterns
Daniela Battaglino,Andrea Frosini,Veronica Guerrini,Simone Rinaldi,Samanta Socci +4 more
- 10 Sep 2014
- Vol. 8668, pp 25-38
TL;DR: The notion of pattern avoidance is used in order to recognize or describe families of polyominoes defined by means of geometrical constraints or combinatorial properties, so that to be able to describe more families ofpolyominoe known in the literature.
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Abstract: The notion of a pattern within a binary picture (polyomino) has been introduced and studied in [3], and resembles the notion of pattern containment within permutations The main goal of this paper is to extend the studies of [3] by adopting a more geometrical approach: we use the notion of pattern avoidance in order to recognize or describe families of polyominoes defined by means of geometrical constraints or combinatorial properties Moreover, we extend the notion of pattern in a polyomino, by introducing generalized polyomino patterns, so that to be able to describe more families of polyominoes known in the literature
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Citations
•Dissertation
Énumération de polyominos définis en terme d'évitement de motif ou de contraintes de convexité
Daniela Battaglino
- 26 Jun 2014
TL;DR: In this article, the problem of characterising and enumerating sets of polyominoes described in terms of some constraints, defined either by convexity or by pattern containment, is considered.
3
Geometric properties of matrices induced by pattern avoidance
TL;DR: This paper uses submatrix avoidance to describe families of polyominoes which, in the literature, are usually defined by means of the geometric constraints of convexity, k-conveXity, and directedness, and studies how these constraints can be imposed on matrices by using subMatrix avoidance.
1
The Number of Snakes in a Box
Christian Barrientos,Sarah Minion +1 more
- 25 Dec 2018
TL;DR: In this paper, the enumeration of two subfamilies of the family of snake polyominoes, stairs and snakes of height 2, was studied from a graph theoretical perspective, using classical ideas, as symmetries, and a new approach that connects these snakes with the partitions of integers.
References
The Art in Computer Programming
Andrew Hunt,Dave Thomas +1 more
- 01 Jan 2001
TL;DR: Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.
Mesh patterns and the expansion of permutation statistics as sums of permutation patterns
Petter Brändén,Anders Claesson +1 more
TL;DR: In this article, a permutation statistic f : G -> C may be represented uniquely as a linear combination of (classical) permutation patterns: f = Sigma(tau) lambda(f) tau)tau.
•Journal Article
Pattern avoidance in set partitions
TL;DR: In this article, the number of set partitions that avoid certain specic patterns is enumerated and characterized, and a notion of pattern in a set partition is proposed based on its restricted growth function.
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•Posted Content
Pattern Avoidance in Set Partitions
TL;DR: This work enumerate and characterize those partitions avoiding any partition of a 3-element set which avoid certain specic patterns, and concludes that the corresponding sequences are P-recursive.
72
Combinatorial aspects of L-convex polyominoes
TL;DR: The paper proves bijectively that the number f"n of L-convex polyominoes with perimeter 2(n+2) satisfies the linear recurrence relation f" n+"2=4f"n"+"1-2f"N, by first establishing a recurrence of the same form for the cardinality of the ''2-compositions'' of a natural number n.
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