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

3 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In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula.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

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Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.

Keywords

Aztec diamonds
Aztec rectangles
Domino tilings
Monotone triangles

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10.1016/j.disc.2015.12.027

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abstract = "In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula.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.",

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KW - Aztec rectangles

KW - Domino tilings

KW - Monotone triangles

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

Abstract

Bibliographical note

Keywords

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