A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombus
| dc.creator | Krattenthaler, Christian | |
| dc.date | 2001-01-01 | |
| dc.date | 2001-07-13 | |
| dc.date.accessioned | 2026-07-07T04:39:28Z | |
| dc.date.available | 2026-07-07T04:39:28Z | |
| dc.description | We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+c,2n+a,2n+b,2n+c$ contains the (horizontal) rhombus with coordinates $(2n+x,2n+y)$ is equal to ${1/3} + g_{a,b,c,x,y}(n) {\binom {2n}{n}}^3 / \binom {6n}{3n}$, where $g_{a,b,c,x,y}(n)$ is a rational function in $n$. Several specific instances of this "1/3-phenomenon" are made explicit. | |
| dc.description | 16 pages, AmS-LaTeX, uses TeXDraw; a few typos corrected | |
| dc.identifier | https://arxiv.org/abs/math/0101009 | |
| dc.identifier | http://arxiv.org/abs/math/0101009 | |
| dc.identifier | in: Number Theory and Discrete Mathematics, A. K. Agarwal et al., eds., Hindustan Book Agency, New Delhi, 2002, pp. 13-30. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60673 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 05A19 05B45 33C20 33C45 52C20 | |
| dc.title | A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombus | |
| dc.type | text |