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

DOI10.1016/j.disc.2015.12.027zbMath1333.05022OpenAlexW2278684317MaRDI QIDQ271618

Tri Lai

Publication date: 7 April 2016

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2015.12.027

zbMATH Keywords

domino tilingsAztec diamondsAztec rectanglesmonotone triangles

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (3)

Refined enumeration of halved monotone triangles and applications to vertically symmetric alternating sign trapezoids ⋮ A shuffling theorem for reflectively symmetric tilings ⋮ Tiling generating functions of halved hexagons and quartered hexagons

Cites Work

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• A bijection proving the Aztec diamond theorem by combing lattice paths
• A simple proof for the number of tilings of quartered Aztec diamonds
• Enumeration of tilings of quartered Aztec rectangles
• Applications of graphical condensation for enumerating matchings and tilings
• Alternating-sign matrices and domino tilings. II
• Alternating sign matrices and descending plane partitions
• Alternating-sign matrices and domino tilings. I
• A simple proof of the Aztec diamond theorem
• Laurent biorthogonal polynomials, \( q\)-Narayana polynomials and domino tilings of the Aztec diamonds
• Aztec diamonds and digraphs, and Hankel determinants of Schröder numbers
• A new simple proof of the Aztec diamond theorem
• Enumeration of perfect matchings in graphs with reflective symmetry

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