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Geometry and Combinatorics of Crystal Melting

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arxiv 1102.0776 v2 pith:QD3EUV5K submitted 2011-02-03 math-ph hep-thmath.COmath.MPmath.PRnlin.SI

Masahito Yamazaki This is my paper · ORCID
classification math-phhep-thmath.COmath.MPmath.PRnlin.SI
keywords modelcrystalinvariantsmeltingaspectscalabi-yaucalledcombinatorial
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues

    hep-th 2025-01 conditional novelty 7.0 of 10

    For quivers satisfying a no-overlap condition, flavored BPS indices are computed by crystal melting derived from Jeffrey-Kirwan residues, and new double quiver algebras are constructed whose crystal representations en...

  2. Quiver BPS Indices from Crystal Profiles

    hep-th 2026-07 conditional novelty 6.5 of 10

    Elliptic genera and lower-dimensional BPS indices equal discrete sums over molecule boundaries in crystals defined by Jeffrey-Kirwan residues, generalizing Nekrasov Young-diagram formulas.

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