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.
ASJC Scopus subject areas
- !!Theoretical Computer Science
- !!Discrete Mathematics and Combinatorics
- !!Computational Theory and Mathematics
Fields of Expertise
- Information, Communication & Computing