### Abstract

Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied.

Original language | English |
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Article number | 055001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 5 |

DOIs | |

Publication status | Published - 8 Feb 2008 |

Externally published | Yes |

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(5), [055001]. https://doi.org/10.1088/1751-8113/41/5/055001