Differential posets and Smith normal forms
| dc.creator | Miller, Alexander | |
| dc.creator | Reiner, Victor | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:47Z | |
| dc.date.available | 2026-07-07T10:17:47Z | |
| dc.description | We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU+tI and UD+tI have Smith normal forms over Z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Y^r. | |
| dc.description | 29 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/0811.1983 | |
| dc.identifier | http://arxiv.org/abs/0811.1983 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173971 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E99 | |
| dc.title | Differential posets and Smith normal forms | |
| dc.type | text |