A generalization of MacMahon's formula

Author:
Mirjana Vuletic

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

Published electronically:
November 19, 2008

MathSciNet review:
2471939

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[BR]**A. Borodin and E. M. Rains,*Eynard-Metha theorem, Schur process, and their Pffafian analogs*; J. Stat. Phys. 121 (2005), no. 3-4, 291-317. MR**2185331 (2006k:82039)****[C]**M. Ciucu,*Plane partitions I: A generalization of MacMahon's formula*; Memoirs of Amer. Math. Soc. 178 (2005), no. 839, 107-144.**[FW]**O. Foda and M. Wheeler,*BKP Plane Partitions*; J. High Energy Phys. JHEP01(2007)075. MR**2285934****[HH]**P. N. Hoffman and J. F. Humphreys,*Projective representations of the symmetric groups- Q-functions and shifted tableaux*, Clarendon Press, Oxford, 1992MR**1205350 (94f:20027)****[Mac]**I. G. Macdonald,*Symmetric functions and Hall polynomials*; 2nd edition, Oxford University Press, New York, 1995. MR**1354144 (96h:05207)****[OR]**A. Okounkov and N. 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 (2004b:60033)****[S]**R. Stanley,*Enumerative combinatorics*, Cambridge University Press, Cambridge, 1999 MR**1676282 (2000k:05026)****[V]**M. Vuletić,*The Shifted Schur Process and Asymptotics of Large Random Strict Plane Partitions*; Int. Math. Res. Notices (2007), Vol. 2007, article ID rnm043, 53 pages. MR**2349310**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (2000):
05E05,
05A15

Retrieve articles in all journals with MSC (2000): 05E05, 05A15

Additional Information

**Mirjana Vuletic**

Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, California 91125

Email:
vuletic@caltech.edu

DOI:
https://doi.org/10.1090/S0002-9947-08-04753-3

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

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.