Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 917-933 |
| Number of pages | 17 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 113 |
| Issue number | 6 |
| DOIs | |
| State | Published - Aug 2006 |
Bibliographical note
Funding Information:✩ The research of the authors was partially supported by the EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe,” grant HPRN-CT-2001-00272. E-mail addresses: [email protected] (R.M. Adin), [email protected] (F. Brenti), [email protected], [email protected] (Y. Roichman).
Funding
✩ The research of the authors was partially supported by the EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe,” grant HPRN-CT-2001-00272. E-mail addresses: [email protected] (R.M. Adin), [email protected] (F. Brenti), [email protected], [email protected] (Y. Roichman).
| Funders | Funder number |
|---|---|
| European Commission | HPRN-CT-2001-00272 |
Keywords
- Descent class
- Length
- Major index
- Permutation statistics
- Signed permutations