The site-perimeter of bargraphs

Authors:
M. Bousquet-Mélou;A. Rechnitzer
Affiliations:
CNRS, LaBRI, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence cedex, France;Department of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
Venue:
Advances in Applied Mathematics
Year:
2003

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Abstract

The site-perimeter enumeration of polyominoes that are both column- and row-convex is a well understood problem that always yields algebraic generating functions. Counting more general families of polyominoes is a far more difficult problem. Here we enumerate (by their site-perimeter) the simplest family of polyominoes that are not fully convex-bargraphs. The generating function we obtain is of a type that, to our knowledge, has never been encountered so far in the combinatorics literature: a q-series into which an algebraic series has been substituted.