Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles

Tri Lai

doi:10.1016/j.disc.2015.12.027

Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles

Tri Lai

Institute for Mathematics and its Applications

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

2 Scopus citations

Abstract

In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.

Original language	English (US)
Pages (from-to)	1512-1518
Number of pages	7
Journal	Discrete Mathematics
Volume	339
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2015.12.027
State	Published - May 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:
© 2016 Elsevier B.V. All rights reserved.

Keywords

Aztec diamonds
Aztec rectangles
Domino tilings
Monotone triangles

Publisher link

10.1016/j.disc.2015.12.027

Find It

Find It at U of M Libraries

Cite this

@article{1ba61eb45bc4451d9c9632441f32d8f2,

title = "Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles",

abstract = "In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.",

keywords = "Aztec diamonds, Aztec rectangles, Domino tilings, Monotone triangles",

author = "Tri Lai",

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: {\textcopyright} 2016 Elsevier B.V. All rights reserved.",

year = "2016",

month = may,

day = "6",

doi = "10.1016/j.disc.2015.12.027",

language = "English (US)",

volume = "339",

pages = "1512--1518",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "5",

}

TY - JOUR

T1 - Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles

AU - Lai, Tri

N1 - 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: © 2016 Elsevier B.V. All rights reserved.

PY - 2016/5/6

Y1 - 2016/5/6

N2 - In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.

AB - In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.

KW - Aztec diamonds

KW - Aztec rectangles

KW - Domino tilings

KW - Monotone triangles

UR - http://www.scopus.com/inward/record.url?scp=84957998822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957998822&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2015.12.027

DO - 10.1016/j.disc.2015.12.027

M3 - Article

AN - SCOPUS:84957998822

SN - 0012-365X

VL - 339

SP - 1512

EP - 1518

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 5

ER -

Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this