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.

PACS numbers: 02.10.Ox, 05.50.+q, 05.70.Jk

Print publication: Issue 5 (8 February 2008)
Received 25 May 2007, in final form 1 November 2007
Published 23 January 2008