## Abstract

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
_{1}n
^{−1}exp(c
_{2}n
^{1/2}) to c
_{3}n
^{−49/72}exp(c
_{4}n
^{2/3}+c
_{5}n
^{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 language | English |
---|---|

Article number | 105363 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 178 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

- 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