3-enumerated alternating sign matrices
| dc.creator | Stroganov, Yu. G. | |
| dc.date | 2003-04-01 | |
| dc.date.accessioned | 2026-07-07T04:29:57Z | |
| dc.date.available | 2026-07-07T04:29:57Z | |
| dc.description | Let $A(n,r;3)$ be the total weight of the alternating sign matrices of order $n$ whose sole `1' of the first row is at the $r^{th}$ column and the weight of an individual matrix is $3^k$ if it has $k$ entries equal to -1. Define the sequence of the generating functions $G_n(t)=\sum_{r=1}^n A(n,r;3)t^{r-1}$. Results of two different kind are obtained. On the one hand I made the explicit expression for the even subsequence $G_{2ν}(t)$ in terms of two linear homogeneous second order recurrence in $ν$ (Theorem 1). On the other hand I brought to light the nice connection between the neighbouring functions $G_{2ν+1}(t)$ and $G_{2ν}(t)$ (Theorem 2). The 3-enumeration $A(n;3) \equiv G_n(1)$ which was found by Kuperberg is reproduced as well. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0304004 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0304004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57347 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Combinatorics | |
| dc.title | 3-enumerated alternating sign matrices | |
| dc.type | text |