Exact generating function for 2-convex polygons

W. R.G. James, I. Jensen, A. J. Guttmann

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Article number055001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number5
Publication statusPublished - 8 Feb 2008
Externally publishedYes


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