Lambda-determinants and domino-tilings
| dc.creator | Propp, James | |
| dc.date | 2004-06-15 | |
| dc.date.accessioned | 2026-07-07T05:09:15Z | |
| dc.date.available | 2026-07-07T05:09:15Z | |
| dc.description | Consider the $2n$-by-$2n$ matrix $M=(m_{i,j})_{i,j=1}^{2n}$ with $m_{i,j} = 1$ for $i,j$ satisfying $|2i-2n-1|+|2j-2n-1| \leq 2n$ and $m_{i,j} = 0$ for all other $i,j$, consisting of a central diamond of 1's surrounded by 0's. When $n \geq 4$, the $λ$-determinant of the matrix $M$ (as introduced by Robbins and Rumsey) is not well-defined. However, if we replace the 0's by $t$'s, we get a matrix whose $λ$-determinant is well-defined and is a polynomial in $λ$ and $t$. The limit of this polynomial as $t \to 0$ is a polynomial in $λ$ whose value at $λ=1$ is the number of domino tilings of a $2n$-by-$2n$ square. | |
| dc.description | 4 pages; to appear in a special issue of Advances in Applied Mathematics honoring David P. Robbins | |
| dc.identifier | https://arxiv.org/abs/math/0406301 | |
| dc.identifier | http://arxiv.org/abs/math/0406301 | |
| dc.identifier | Advances in Applied Mathematics, Volume 34, Issue 4, May 2005, pp. 871-879 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71563 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A99 | |
| dc.title | Lambda-determinants and domino-tilings | |
| dc.type | text |