A generalization of Aztec diamond theorem, part II

Tri Lai

doi:10.1016/j.disc.2015.10.045

A generalization of Aztec diamond theorem, part II

Tri Lai

Institute for Mathematics and its Applications

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The author gave a proof of a generalization of the Aztec diamond theorem for a family of 4-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in Lai (2014) by using a bijection between tilings and non-intersecting lattice paths. In this paper, we use Kuo graphical condensation to give a new proof.

Original language	English (US)
Pages (from-to)	1172-1179
Number of pages	8
Journal	Discrete Mathematics
Volume	339
Issue number	3
DOIs	https://doi.org/10.1016/j.disc.2015.10.045
State	Published - Mar 6 2016

Bibliographical note

Funding Information:
This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation (grant no. DMS-0931945 ).

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Aztec diamonds
Dual graph
Graphical condensation
Perfect matchings
Tilings

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10.1016/j.disc.2015.10.045

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AB - The author gave a proof of a generalization of the Aztec diamond theorem for a family of 4-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in Lai (2014) by using a bijection between tilings and non-intersecting lattice paths. In this paper, we use Kuo graphical condensation to give a new proof.

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KW - Dual graph

KW - Graphical condensation

KW - Perfect matchings

KW - Tilings

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A generalization of Aztec diamond theorem, part II

Abstract

Bibliographical note

Keywords

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