Geometry and Combinatorics of Crystal Melting

Details Geometry and Combinatorics of Crystal Melting Geometry and Combinatorics of Crystal Melting

2011-02-03

arxiv.org/abs/1102.0776v2

Publ.Res.Inst.Math.Sci.Kyoto B28:193,2011

Physics

Mathematical Physics

21 pages, 6 figures, to appear in RIMS Kokyuroku Bessatsu, based on a talk at "Developments in Quantum Integrable Systems," RI

Scientific paper

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.

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