A simple proof of the Aztec diamond theorem

Sen Peng Eu; Tung Shan Fu

doi:10.37236/1915

A simple proof of the Aztec diamond theorem

Sen Peng Eu^*
, Tung Shan Fu

^*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by means of Hankel determinants of the large and small Schröder numbers.

Original language	English
Journal	Electronic Journal of Combinatorics
Volume	12
Issue number	1 R
DOIs	https://doi.org/10.37236/1915
Publication status	Published - 2005 Apr 20
Externally published	Yes

Keywords

Aztec diamond
Domino tilings
Hankel matrices
Lattice paths
Schröder numbers

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/1915

Cite this

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title = "A simple proof of the Aztec diamond theorem",

abstract = "Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by means of Hankel determinants of the large and small Schr{\"o}der numbers.",

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author = "Eu, \{Sen Peng\} and Fu, \{Tung Shan\}",

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AB - Based on a bijection between domino tilings of an Aztec diamond and non-intersecting lattice paths, a simple proof of the Aztec diamond theorem is given by means of Hankel determinants of the large and small Schröder numbers.

KW - Aztec diamond

KW - Domino tilings

KW - Hankel matrices

KW - Lattice paths

KW - Schröder numbers

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JF - Electronic Journal of Combinatorics

IS - 1 R

ER -

A simple proof of the Aztec diamond theorem

Abstract

Keywords

ASJC Scopus subject areas

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