Snake Polyominoes of Maximal Area in a Rectangle
This paper presents an algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes for certain dimensions.
This paper presents a novel algorithm to generate snake-like polyominoes within a given rectangle and provides exact formulas for the maximal area of such polyominoes, which is a new contribution to the field.
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Applications
- →Computer graphics
- →Discrete geometry
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Abstract
More Like ThisGiven a discrete rectangle R of dimensions h x w, let W be the set of snake-like polyominoes contained in R represented as binary matrices, i.e. polyominoes whose underlying simple graph is a chain with respect to the 4-adjacency relation. We present an algorithm that generates W for any h and w. Also, let a be the maximal area that can be realized by an element of W. We provide exact formulas of a for h <= 5 and any w.