Geometry and Combinatorics of Crystal Melting
Mathematical Physics
2015-03-18 v2 High Energy Physics - Theory
Combinatorics
math.MP
Probability
Exactly Solvable and Integrable Systems
Abstract
We survey geometrical and especially combinatorial aspects of generalized Donaldson-Thomas invariants (also called BPS invariants) for toric Calabi-Yau manifolds, emphasizing the role of plane partitions and their generalizations in the recently proposed crystal melting model. We also comment on equivalence with a vicious walker model and the matrix model representation of the partition function.
Keywords
Cite
@article{arxiv.1102.0776,
title = {Geometry and Combinatorics of Crystal Melting},
author = {Masahito Yamazaki},
journal= {arXiv preprint arXiv:1102.0776},
year = {2015}
}
Comments
21 pages, 6 figures, to appear in RIMS Kokyuroku Bessatsu, based on a talk at "Developments in Quantum Integrable Systems," RIMS, Kyoto University, June 2010; v2: typos corrected