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Boletín de la Sociedad Matemática Mexicana

, Volume 25, Issue 3, pp 461–479 | Cite as

Parabolically induced functions and equidistributed pairs

  • Paolo SentinelliEmail author
Original Article

Abstract

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.

Keywords

Coxeter groups Mahonian pairs Major index 

Mathematics Subject Classification

05A05 05E15 06A07 20F55 

Notes

Acknowledgements

I would like to thank the anonymous referee for the meticulous revision and for some useful remarks. Supported by Postdoctorado FONDECYT-CONICYT 3160010.

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Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de ChileÑuñoaChile

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