A generalization of MacMahon’s formula
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- by Mirjana Vuletić PDF
- Trans. Amer. Math. Soc. 361 (2009), 2789-2804 Request permission
Abstract:
We generalize the generating formula for plane partitions known as MacMahon’s formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald’s symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon’s formula for strict plane partitions.References
- Alexei Borodin and Eric M. Rains, Eynard-Mehta theorem, Schur process, and their Pfaffian analogs, J. Stat. Phys. 121 (2005), no. 3-4, 291–317. MR 2185331, DOI 10.1007/s10955-005-7583-z
- M. Ciucu, Plane partitions I: A generalization of MacMahon’s formula; Memoirs of Amer. Math. Soc. 178 (2005), no. 839, 107–144.
- Omar Foda and Michael Wheeler, BKP plane partitions, J. High Energy Phys. 1 (2007), 075, 9. MR 2285934, DOI 10.1088/1126-6708/2007/01/075
- P. N. Hoffman and J. F. Humphreys, Projective representations of the symmetric groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1992. $Q$-functions and shifted tableaux; Oxford Science Publications. MR 1205350
- I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995. With contributions by A. Zelevinsky; Oxford Science Publications. MR 1354144
- Andrei Okounkov and Nikolai Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, J. Amer. Math. Soc. 16 (2003), no. 3, 581–603. MR 1969205, DOI 10.1090/S0894-0347-03-00425-9
- Richard P. Stanley, Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. MR 1676282, DOI 10.1017/CBO9780511609589
- Mirjana Vuletić, The shifted Schur process and asymptotics of large random strict plane partitions, Int. Math. Res. Not. IMRN 14 (2007), Art. ID rnm043, 53. MR 2349310, DOI 10.1093/imrn/rnm043
Additional Information
- Mirjana Vuletić
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- Email: vuletic@caltech.edu
- Received by editor(s): August 6, 2007
- Received by editor(s) in revised form: January 11, 2008, and February 6, 2008
- Published electronically: November 19, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 2789-2804
- MSC (2000): Primary 05E05, 05A15
- DOI: https://doi.org/10.1090/S0002-9947-08-04753-3
- MathSciNet review: 2471939