The Number of Snakes in a Box
Christian Barrientos,Sarah Minion +1 more
- 25 Dec 2018
- Vol. 1, Iss: 2, pp 145-156
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.
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Abstract: Within the class of polyominoes we work on the enumeration of two subfamilies of the family of snake polyominoes: stairs and snakes of height 2. We consider them from a graph theoretical perspective. In the process of enumeration of these graphs, we use classical ideas, as symmetries, and a new approach that connects these snakes with the partitions of integers.
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References
•Journal Article
A Dynamic Survey of Graph Labeling
TL;DR: In this survey I have collected everything I could find on graph labelings techniques that have appeared in journals that are not widely available.
Partially directed snake polyominoes
TL;DR: In this paper, the authors introduce and investigate the family of partially directed snake polyominoes and establish recurrences, functional equations and generating functions with respect to length and height for two-dimensional, three-dimensional and four-dimensional partially-directed snake polyomorphies.
5
Snakes: from Graceful to Harmonious.
Christian Barrientos,Sarah Minion +1 more
- 01 Jan 2017
TL;DR: It is proved that all quadrilateral snakes, all snake polyominoes, all hybrid quadr bilateral snakes, and all straight simple polyominal caterpillars are harmonious graphs.
3
Binary Pictures with Excluded Patterns
Daniela Battaglino,Andrea Frosini,Veronica Guerrini,Simone Rinaldi,Samanta Socci +4 more
- 10 Sep 2014
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.