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An algebraic extension of the MacMahon Master Theorem
Author(s):
Pavel
Etingof;
Igor
Pak
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2279-2288.
MSC (2000):
Primary 16S37;
Secondary 05A30, 05E05, 81S05
Posted:
March 13, 2008
MathSciNet review:
2390493
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Abstract:
We present a new algebraic extension of the classical MacMahon Master Theorem. The basis of our extension is the Koszul duality for non-quadratic algebras defined by Berger. Combinatorial implications are also discussed.
References:
-
- [B]
- R. Berger, Koszulity for nonquadratic algebras, J. Algebra 239 (2001), 705-734. MR 1832913 (2002d:16034)
- [CF]
- P. Cartier and D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, No. 85, Springer, Berlin, 1969; available electronically at http://www.mat.univie.ac.at/~slc/books/cartfoa.html. MR 0239978 (39:1332)
- [DB]
- F. N. David and D. E. Barton, Combinatorial Chance, Hafner, New York, 1962. MR 0155371 (27:5305)
- [FH1]
- D. Foata and G.-N. Han, A new proof of the Garoufalidis-Lê-Zeilberger quantum MacMahon master theorem, J. Algebra 307 (2007), no. 1, 424-431. MR 2278064 (2008b:05008)
- [FH2]
- D. Foata and G.-N. Han, Specializations and extensions of the quantum MacMahon Master Theorem, Linear Algebra Appl. 423 (2007), no. 2-3, 445-455. MR 2312419 (2008c:05012)
- [FZ]
- D. Foata and D. Zeilberger, Laguerre polynomials, weighted derangements, and positivity, SIAM J. Disc. Math. 1 (1988), no. 4, 425-433. MR 968850 (89m:05008)
- [Fr]
- R. Fröberg, Koszul Algebras, Lecture Notes in Pure and Appl. Math., 205, Dekker, New York, 1999, 337-350. MR 1767430 (2001i:16046)
- [GLZ]
- S. Garoufalidis, T. Tq Lê and D. Zeilberger, The quantum MacMahon master theorem, Proc. Natl. Acad. Sci. USA 103 (2006), no. 38, 13928-13931. MR 2270337
- [GJ]
- I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley, New York, 1983. MR 702512 (84m:05002)
- [HL]
- P. H. Hai and M. Lorenz, Koszul algebras and the quantum MacMahon master theorem, Bull. Lond. Math. Soc. 39 (2007), no. 4, 667-676. MR 2346948
- [KP]
- M. Konvalinka and I. Pak, Non-commutative extensions of the MacMahon master theorem, Adv. Math. 216 (2007), no. 1, 29-61. MR 2353248
- [Ma]
- I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, The Clarendon Press, Oxford University Press, New York, 1995. MR 1354144 (96h:05207)
- [MM]
- P. A. MacMahon, Combinatory Analysis, 2 vols., Cambridge University Press, 1915 and 1916; reprinted in one volume by Chelsea, New York, 1960. MR 0141605 (25:5003)
- [PP]
- A. Polishchuk and L. Positselski, Quadratic Algebras, University Lecture Series, 37, Amer. Math. Soc., Providence, RI, 2005. MR 2177131 (2006f:16043)
- [R]
- N. Roby, Séries de Poincaré des algèbres
 -extérieures (in French), Bull. Sci. Math. (2) 95 (1971), 3-14. MR 0282861 (44:95) - [S]
- R. P. Stanley, Enumerative Combinatorics, vols. 1, 2, Cambridge Studies in Advanced Mathematics, 49, 62, Cambridge University Press, Cambridge, UK, 1997, 1999. MR 1442260 (98a:05001), MR 1676282 (2000k:05026)
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Additional Information:
Pavel
Etingof
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
etingof@math.mit.edu
Igor
Pak
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
pak@math.mit.edu
DOI:
10.1090/S0002-9939-08-09017-5
PII:
S 0002-9939(08)09017-5
Received by editor(s):
August 1, 2006
Posted:
March 13, 2008
Communicated by:
Jim Haglund
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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