Combinatorics of diagonally convex directed polyominoes
type: Item
instance of: scholarly article
title: Combinatorics of diagonally convex directed polyominoes
zbMATH Open document ID: 0857.05020
DOI: 10.1016/S0012-365X(96)83012-3
author: Feretić
author: Dragutin Svrtan
published in: Discrete Mathematics
publication date: 1996-11-27T00:00:00Z
review text: The authors consider the problem of finding a generating function for diagonally convex directed (dcd) polyominoes. These are first defined and shown to be in correspondence (not (1-1)) with lattice paths wholly below the line \(y={1\over 2} x\) and also with ternary trees, to which ``1-source'' polyominoes are shown to be in 1-1 correspondence. The main result of the paper is to extend the enumeration by perimeter of dcd polyominoes to the multisource case. The formula is confined by another method, and a start is made on the problem of finding a ``\(q\)-enumeration'' generating function, enumeration by perimeter and area. This is accomplished for ``1-source'' polyominoes, but the general case is deferred to a further paper. Reviewer's note: This is one of the most skilful uses of generating functions and transformations I have ever seen. It is comparable with MacMahon's classic work.
Mathematics Subject Classification ID: 05B50
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 935377
zbMATH Keywords: generating function
zbMATH Keywords: diagonally convex directed (dcd) polyominoes
zbMATH Keywords: lattice paths
reviewed by: H. N. V. Temperley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 935377