English

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

R2 v1 2026-06-21T17:21:20.566Z