A generalized Major index statistic
| dc.creator | Assaf, Sami | |
| dc.date | 2008-07-02 | |
| dc.date.accessioned | 2026-07-07T09:48:05Z | |
| dc.date.available | 2026-07-07T09:48:05Z | |
| dc.description | Inspired by the $k$-inversion statistic for LLT polynomials, we define a $k$-inversion number and $k$-descent set for words. Using these, we define a new statistic on words, called the $k$-major index, that interpolates between the major index and inversion number. We give a bijective proof that the $k$-major index is equidistributed with the major index, generalizing a classical result of Foata and rediscovering a result of Kadell. Inspired by recent work of Haglund and Stevens, we give a partial extension of these definitions and constructions to standard Young tableaux. Finally, we give an application to Macdonald polynomials made possible through connections with LLT polynomials. | |
| dc.description | 12 pages, 4 figures, to appear in SLC | |
| dc.identifier | https://arxiv.org/abs/0807.0433 | |
| dc.identifier | http://arxiv.org/abs/0807.0433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164081 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15; 05A05, 05A19, 05E05, 05E10 | |
| dc.title | A generalized Major index statistic | |
| dc.type | text |