COMBINATORICS AND N-KOSZUL ALGEBRAS
2008 ◽
Vol 05
(08)
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pp. 1205-1214
Keyword(s):
New Type
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The numerical Hilbert series combinatorics for quadratic Koszul algebras was extended to N-Koszul algebras by Dubois-Violette and Popov [9]. In this paper, we give a striking application of this extension when the relations of the algebra are all the antisymmetric tensors of degree N over given variables. Furthermore, we present a new type of Hilbert series combinatorics, called comodule Hilbert series combinatorics, and due to Hai, Kriegk and Lorenz [15]. When the relations are all the antisymmetric tensors, a natural generalization of the MacMahon Master Theorem (MMT) is obtained from the comodule level, the original MMT corresponding to N = 2 and to polynomial algebras.
2007 ◽
Vol 39
(4)
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pp. 667-676
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1986 ◽
Vol 44
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pp. 632-633
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