A complementation theorem for perfect matchings of graphs having a cellular completion
type: Item
instance of: scholarly article
title: A complementation theorem for perfect matchings of graphs having a cellular completion
zbMATH Open document ID: 0897.05063
author: Mihai Ciucu
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-10-05T00:00:00Z
review text: A graph whose edges can be partitioned into 4-cycles in such a way that each vertex is contained in at most two 4-cycles is called a cellular graph. The author gives a ``complementation theorem'' for enumerating the matchings of certain subgraphs of cellular graphs. He applies this theorem to obtain a number of results which include a new proof of Stanley's version of the Aztec diamond theorem, a weighted generalization of a result of Knuth which deals with spanning trees of Aztec diamond graphs, a combinatorial proof of Yang's enumeration of matchings in fortress graphs, and proofs for certain identities of Jockusch and Propp which deal with the numbers of matchings of three kinds of quartered Aztec diamonds.
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 1123547
zbMATH Keywords: perfect matching
zbMATH Keywords: Aztec diamond
zbMATH Keywords: cellular graph
reviewed by: Michael Raines
describes a project that uses: ROBBINS
MaRDI profile type: Publication
OpenAlex ID: W2073445741
cites work: Perfect matchings of cellular graphs
cites work: Enumeration of perfect matchings in graphs with reflective symmetry
cites work: Alternating-sign matrices and domino tilings. I
cites work: Aztec diamonds, checkerboard graphs, and spanning trees
cites work: Q4880965
cites work: Q3880849
cites work: Alternating sign matrices and descending plane partitions
cites work: Conway's Tiling Groups
cites work: Proof of the alternating sign matrix conjecture
DOI: 10.1006/JCTA.1997.2799
description: scientific article; zbMATH DE number 1123547