期刊
JOURNAL OF COMBINATORIAL THEORY SERIES A
卷 116, 期 2, 页码 334-350出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcta.2008.06.006
关键词
Dimer model; Shuffling; Donaldson-Thomas theory; Generating functions; Partition functions; Pyramid partitions
类别
We verify a recent conjecture of Kenyon/Szendroi by computing the generating function for pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson-Thomas theory of a non-commutative resolution of the conifold singularity {X1X2-X3X4 = 0} subset of C-4. The proof does not require algebraic geometry; it uses a modified version of the domino shuffling algorithm of Elkies, Kuperberg, Larsen and Propp [Noam Elkies, Greg Kuperberg, Michael Larsen, James Propp, Alternating sign matrices and domino tilings. II, J. Algebraic Combin. 1 (3) (1992) 219-234]. (C) 2008 Elsevier Inc. All rights reserved.
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