ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration
| dc.creator | Andrews, George E. | |
| dc.creator | Krattenthaler, Christian | |
| dc.creator | Orsina, Luigi | |
| dc.creator | Papi, Paolo | |
| dc.date | 2000-04-17 | |
| dc.date.accessioned | 2026-07-07T04:34:46Z | |
| dc.date.available | 2026-07-07T04:34:46Z | |
| dc.description | We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of $sl(n+1,\Bbb C)$. We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. We study the relationships between these results and the combinatorics of Dyck paths, based upon a remarkable bijection between ad-nilpotent ideals and Dyck paths. Finally, we propose a (q,t)-analogue of the Catalan number $C_n$. These (q,t)-Catalan numbers count on the one hand ad-nilpotent ideals with respect to dimension and class of nilpotence, and on the other hand admit interpretations in terms of natural statistics on Dyck paths. | |
| dc.description | 19 pages, AmS-TeX | |
| dc.identifier | https://arxiv.org/abs/math/0004107 | |
| dc.identifier | http://arxiv.org/abs/math/0004107 | |
| dc.identifier | Trans. Amer. Math. Soc. 354 (2002), 3835-3853. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59035 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 17B20 (Primary) 05A15 05A19 05E15 17B30 (Secondary) | |
| dc.title | ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumeration | |
| dc.type | text |