Abstract
In 1938, Pólya stated an identity involving the perimeter and area generating function for parallelogram polyominoes. To obtain that identity, Pólya presumably considered festoons . A festoon (so named by Flajolet) is a closed path w which can be written as w = uv , where each step of u is either (1,0) or (0,1), and each step of v is either (−1,0) or (0,−1). In this paper, we introduce four new festoon-like objects. As a result, we obtain explicit expressions (and not just identities) for the generating functions of parallelogram polyominoes, directed convex polyominoes, and convex polyominoes.
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