A remark on certain restricted plane partitions and crystal melting model
Abstract
In this paper, we provide formulas calculating the partition functions of two types of plane partitions using the crystal melting model method introduced by Okounkov, Reshetikhin and Vafa. As applications, we obtain a product formula for the partition function of the plane partitions with a limit shape boundary. A corollary of this formula is the demonstration of the equivalence between this partition function and the openclosed string amplitude of the double$\mathbb{P}^1$ model. We also derive a product formula for the partition function of symmetric plane partitions with a limit shape boundary.
 Publication:

arXiv eprints
 Pub Date:
 December 2023
 DOI:
 10.48550/arXiv.2312.02749
 arXiv:
 arXiv:2312.02749
 Bibcode:
 2023arXiv231202749Y
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Combinatorics
 EPrint:
 29 pages