A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Schützenberger gave a remarkable refinement and proved that these parameters are equi-distributed over inverse descent classes, implying bivariate equi-distribution identities. Type B analogues of these results, refinements and consequences are given in this paper.
|Title of host publication
|16th Conference in Formal Power Series and Algebraic Combinatorics
|Published - 2004
Bibliographical noteJournal of Combinatorial Theory, Series A
Volume 113, Issue 6, August 2006, Pages 917–933;
Place of conference:University of British Columbia, Vancouver B. C., Canada.