The asymptotics of plane partitions with fixed volumes of diagonal parts

DOI10.1007/s10958-021-05495-zzbMath1471.05006OpenAlexW3196796488MaRDI QIDQ1979502

Yanyan Li

Publication date: 3 September 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05495-z

zbMATH Keywords

enumeration of plane partitionsgenerating function of plane partitions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Partitions of sets (05A18) Combinatorial aspects of partitions of integers (05A17) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

• Plane partition polynomial asymptotics
• Statistical mechanics of combinatorial partitions, and their limit shapes
• On Mayer's theory of cluster expansions
• The q-analogue of Stirling's formula
• The enumeration of plane partitions via the Burge correspondence
• Generating functions for plane partitions of a given shape
• Counting partitions inside a rectangle
• Correlation functions of XX0 Heisenberg chain, \(q\)-binomial determinants, and random walks
• The conjugate trace and trace of a plane partition
• Integrable models and combinatorics
• The phase model and the norm-trace generating function of plane partitions
• ASYMPTOTIC PARTITION FORMULAE
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• The partition function of the four-vertex model in inhomogeneous external field and trace statistics
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