We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore we generalize the main identity of Chow and Gessel by computing the four-variate generating series of descents, major index, length, and number of negative entries over Coxeter groups of type B and D.
Biagioli R, Zeng J (2010). On some analogous of Carlitz’s identity for the hyperoctahedral group. SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE, 61, 1-13.
On some analogous of Carlitz’s identity for the hyperoctahedral group
Biagioli R;
2010
Abstract
We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore we generalize the main identity of Chow and Gessel by computing the four-variate generating series of descents, major index, length, and number of negative entries over Coxeter groups of type B and D.File in questo prodotto:
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