On the number of plane partitions and non isomorphic subgroup towers of abelian groups
| dc.creator | Andersson, Johan | |
| dc.creator | Snellman, Jan | |
| dc.date | 2006-07-27 | |
| dc.date.accessioned | 2026-07-07T07:21:01Z | |
| dc.date.available | 2026-07-07T07:21:01Z | |
| dc.description | We study the number of $k \times r$ plane partitions, weighted on the sum of the first row. Using Erhart reciprocity, we prove an identity for the generating function. For the special case $k=1$ this result follows from the classical theory of partitions, and for $k=2$ it was proved in Andersson-Bhowmik with another method. We give an explicit formula in terms of Young tableaux, and study the corresponding zeta-function. We give an application on the average orders of towers of abelian groups. In particular we prove that the number of isomorphism classes of ``subgroups of subgroups of ... ($k-1$ times) ... of abelian groups'' of order at most $N$ is asymptotic to $c_k N (\log N)^{k-1}$. This generalises results from Erd{\H o}s-Szekeres and Andersson-Bhowmik where the corresponding result was proved for $k=1$ and $k=2$. | |
| dc.description | 20 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607698 | |
| dc.identifier | http://arxiv.org/abs/math/0607698 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115156 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11M41; 20K01, 05A17 | |
| dc.title | On the number of plane partitions and non isomorphic subgroup towers of abelian groups | |
| dc.type | text |