Computing a pyramid partition generating function with dimer shuffling

Citations of this article
Mendeley users who have this article in their library.


We verify a recent conjecture of Kenyon/Szendro{combining double acute accent}i 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 {x1 x2 - x3 x4 = 0} ⊂ C4. 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]. © 2008 Elsevier Inc. All rights reserved.




Young, B. (2009). Computing a pyramid partition generating function with dimer shuffling. Journal of Combinatorial Theory. Series A, 116(2), 334–350.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free