Double Aztec rectangles

Tri Lai

doi:10.1016/j.aam.2015.11.001

Double Aztec rectangles

Tri Lai

Institute for Mathematics and its Applications

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

4 Scopus citations

Abstract

We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a simple product formula for the generating functions of the tilings of the new regions, which involves the statistics as in the Aztec diamond theorem (Elkies et al. (1992) [2,3]). Moreover, we consider the connection between the generating function and MacMahon's q-enumeration of plane partitions fitting in a given box.

Original language	English (US)
Pages (from-to)	1-17
Number of pages	17
Journal	Advances in Applied Mathematics
Volume	75
DOIs	https://doi.org/10.1016/j.aam.2015.11.001
State	Published - Apr 1 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Domino tilings
Lozenge tilings
Perfect matchings
Plane partitions
Urban renewal

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.aam.2015.11.001

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AB - We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a simple product formula for the generating functions of the tilings of the new regions, which involves the statistics as in the Aztec diamond theorem (Elkies et al. (1992) [2,3]). Moreover, we consider the connection between the generating function and MacMahon's q-enumeration of plane partitions fitting in a given box.

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KW - Lozenge tilings

KW - Perfect matchings

KW - Plane partitions

KW - Urban renewal

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ER -

Double Aztec rectangles

Abstract

Bibliographical note

Keywords

UN SDGs

Access

OpenUrl availability

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