From Aztec diamonds to pyramids: Steep tilings

DOI10.1090/tran/7169zbMath1362.05033arXiv1407.0665OpenAlexW3104118203MaRDI QIDQ5347286

Guillaume Chapuy, Jérémie Bouttier, Sylvie Corteel

Publication date: 23 May 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0665

zbMATH Keywords

domino tilings

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Combinatorial probability (60C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Combinatorial aspects of tessellation and tiling problems (05B45)

Related Items (16)

Domino statistics of the two-periodic Aztec diamond ⋮ Asymptotics of random domino tilings of rectangular Aztec diamonds ⋮ The free boundary Schur process and applications. I ⋮ Asymptotics of pure dimer coverings on rail yard graphs ⋮ On the domino shuffle and matrix refactorizations ⋮ Rogers-Ramanujan identities and the Robinson-Schensted-Knuth correspondence ⋮ Free fermion six vertex model: symmetric functions and random domino tilings ⋮ The periodic Schur process and free fermions at finite temperature ⋮ Binomial ideals of domino tilings ⋮ Trace identities for the topological vertex ⋮ The free boundary Schur process and applications ⋮ Fluctuations of particle systems determined by Schur generating functions ⋮ Airy point process at the liquid-gas boundary ⋮ The \(A_2\) Rogers-Ramanujan identities revisited ⋮ Periodic Pólya urns, the density method and asymptotics of Young tableaux ⋮ Fourier transform on high-dimensional unitary groups with applications to random tilings

Cites Work

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• Anisotropic growth of random surfaces in \({2+1}\) dimensions
• Schur dynamics of the Schur processes
• Dimers on rail yard graphs
• Alternating-sign matrices and domino tilings. II
• Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes
• Non-commutative Donaldson-Thomas invariants and the conifold
• Generating functions for colored 3D Young diagrams and the Donaldson-Thomas invariants of orbifolds
• Computing a pyramid partition generating function with dimer shuffling
• Alternating-sign matrices and domino tilings. I
• Local statistics for random domino tilings of the Aztec diamond
• A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin
• Tacnode GUE-minor processes and double Aztec diamonds
• Plane overpartitions and cylindric partitions
• Double Aztec diamonds and the tacnode process
• Macdonald processes
• Coupling functions for domino tilings of Aztec diamonds
• Periodic Schur process and cylindric partitions
• Eynard-Mehta theorem, Schur process, and their Pfaffian analogs
• Conway's Tiling Groups
• A generalization of MacMahon’s formula
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• Arctic curves of the octahedron equation
• Infinite wedge and random partitions

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