Phase transitions from exp⁡(n1/2) to exp⁡(n2/3) in the asymptotics of banded plane partitions

W. Fang*, H.-K. Hwang, M. Kang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We examine the asymptotics of a class of banded plane partitions under a varying bandwidth parameter m, and clarify the transitional behavior for large size n and increasing m=m(n) to be from c 1n −1exp⁡(c 2n 1/2) to c 3n −49/72exp⁡(c 4n 2/3+c 5n 1/3) for some explicit coefficients c 1,…,c 5. The method of proof, which is a unified saddle-point analysis for all phases, is general and can be extended to other classes of plane partitions.

Original languageEnglish
Article number105363
JournalJournal of Combinatorial Theory. Series B
Publication statusPublished - 2021


  • Asymptotics
  • Banded plane partition
  • Integer partition
  • Phase transition
  • Plane partition
  • Saddle point method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Fields of Expertise

  • Information, Communication & Computing


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