Enumeration of hybrid domino-lozenge tilings

Tri Lai

doi:10.1016/j.jcta.2013.10.001

Enumeration of hybrid domino-lozenge tilings

Tri Lai

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

12 Scopus citations

Abstract

We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

Original language	English (US)
Pages (from-to)	53-81
Number of pages	29
Journal	Journal of Combinatorial Theory. Series A
Volume	122
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2013.10.001
State	Published - Feb 2014
Externally published	Yes

Keywords

Aztec diamonds
Aztec rectangles
Dual graphs
Perfect matchings
Quasi-hexagons
Tilings

Access

10.1016/j.jcta.2013.10.001

OpenUrl availability

Full text

Cite this

@article{876783b691644a20889e143e21426647,

title = "Enumeration of hybrid domino-lozenge tilings",

abstract = "We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.",

keywords = "Aztec diamonds, Aztec rectangles, Dual graphs, Perfect matchings, Quasi-hexagons, Tilings",

author = "Tri Lai",

year = "2014",

month = feb,

doi = "10.1016/j.jcta.2013.10.001",

language = "English (US)",

volume = "122",

pages = "53--81",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Enumeration of hybrid domino-lozenge tilings

AU - Lai, Tri

PY - 2014/2

Y1 - 2014/2

N2 - We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

AB - We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

KW - Aztec diamonds

KW - Aztec rectangles

KW - Dual graphs

KW - Perfect matchings

KW - Quasi-hexagons

KW - Tilings

UR - http://www.scopus.com/inward/record.url?scp=84886695681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886695681&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2013.10.001

DO - 10.1016/j.jcta.2013.10.001

M3 - Article

AN - SCOPUS:84886695681

SN - 0097-3165

VL - 122

SP - 53

EP - 81

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -

Enumeration of hybrid domino-lozenge tilings

Abstract

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this