# Domino tilings of the expanded Aztec diamond

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The expanded Aztec diamond is a generalized version of the Aztec diamond, with an arbitrary number of long columns and long rows in the middle. In this paper, we count the number of domino tilings of the expanded Aztec diamond. The exact number of domino tilings is given by recurrence relations of state matrices by virtue of the state matrix recursion algorithm, recently developed by the author to solve various two-dimensional regular lattice model enumeration problems.

Original language English Discrete Mathematics https://doi.org/10.1016/j.disc.2017.10.016 Accepted/In press - 2017 Jan 1

### Fingerprint

Domino Tilings
Strombus or kite or diamond
Diamonds
Recurrence relation
Lattice Model
Recursion
Enumeration
Count
Arbitrary

### Keywords

• Aztec diamond
• Dimer covering
• Domino tiling
• Perfect matching

### ASJC Scopus subject areas

• Theoretical Computer Science
• Discrete Mathematics and Combinatorics

### Cite this

In: Discrete Mathematics, 01.01.2017.

Research output: Contribution to journalArticle

title = "Domino tilings of the expanded Aztec diamond",
abstract = "The expanded Aztec diamond is a generalized version of the Aztec diamond, with an arbitrary number of long columns and long rows in the middle. In this paper, we count the number of domino tilings of the expanded Aztec diamond. The exact number of domino tilings is given by recurrence relations of state matrices by virtue of the state matrix recursion algorithm, recently developed by the author to solve various two-dimensional regular lattice model enumeration problems.",
keywords = "Aztec diamond, Dimer covering, Domino tiling, Perfect matching",
author = "Oh, {Seung Sang}",
year = "2017",
month = "1",
day = "1",
doi = "10.1016/j.disc.2017.10.016",
language = "English",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",

}

TY - JOUR

T1 - Domino tilings of the expanded Aztec diamond

AU - Oh, Seung Sang

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The expanded Aztec diamond is a generalized version of the Aztec diamond, with an arbitrary number of long columns and long rows in the middle. In this paper, we count the number of domino tilings of the expanded Aztec diamond. The exact number of domino tilings is given by recurrence relations of state matrices by virtue of the state matrix recursion algorithm, recently developed by the author to solve various two-dimensional regular lattice model enumeration problems.

AB - The expanded Aztec diamond is a generalized version of the Aztec diamond, with an arbitrary number of long columns and long rows in the middle. In this paper, we count the number of domino tilings of the expanded Aztec diamond. The exact number of domino tilings is given by recurrence relations of state matrices by virtue of the state matrix recursion algorithm, recently developed by the author to solve various two-dimensional regular lattice model enumeration problems.

KW - Aztec diamond

KW - Dimer covering

KW - Domino tiling

KW - Perfect matching

UR - http://www.scopus.com/inward/record.url?scp=85033592817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033592817&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2017.10.016

DO - 10.1016/j.disc.2017.10.016

M3 - Article

AN - SCOPUS:85033592817

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

ER -