Four factorization formulas for plane partitions
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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.References
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Additional Information
- Mihai Ciucu
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 605457
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1841-1856
- MSC (2010): Primary 05A15, 05A17; Secondary 05A19
- DOI: https://doi.org/10.1090/proc/12800
- MathSciNet review: 3460147