Given a function defined over a parabolic subgroup of a Coxeter group, equidistributed with the length, we give a procedure to construct a function over the entire group, equidistributed with the length. Such a procedure permits to define functions equidistributed with the length in all the finite Coxeter groups. We can establish our results in the general setting of graded posets which satisfy some properties. These results apply to some known functions arising in Coxeter groups as the major index, the negative major index and the D-negative major index defined in type A, B, and D, respectively.
Coxeter groups Mahonian pairs Major index
Mathematics Subject Classification
05A05 05E15 06A07 20F55
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I would like to thank the anonymous referee for the meticulous revision and for some useful remarks. Supported by Postdoctorado FONDECYT-CONICYT 3160010.
Adin, R.M., Brenti, F., Roichman, Y.: Descent numbers and major indices for the hyperoctahedral group. Adv. Appl. Math. 27(2–3), 210–224 (2001)MathSciNetCrossRefGoogle Scholar