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Four factorization formulas for plane partitions


Author: Mihai Ciucu
Journal: Proc. Amer. Math. Soc. 144 (2016), 1841-1856
MSC (2010): Primary 05A15, 05A17; Secondary 05A19
DOI: https://doi.org/10.1090/proc/12800
Published electronically: January 20, 2016
MathSciNet review: 3460147
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Abstract: All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing identities connecting the various symmetry classes. We present in this paper four such identities, involving all ten symmetry classes. We discuss their proofs and generalizations. The main result of this paper is to give a generalization of one of them, in the style of the identity presented in ``A factorization theorem for rhombus tilings,'' M. Ciucu and C. Krattenthaler, arXiv:1403.3323.


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Additional Information

Mihai Ciucu
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

DOI: https://doi.org/10.1090/proc/12800
Received by editor(s): October 16, 2014
Published electronically: January 20, 2016
Additional Notes: This research was supported in part by NSF grant DMS-1101670
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2016 American Mathematical Society

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