𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Enumeration of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus in the Centre

✍ Scribed by Ilse Fischer

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
418 KB
Volume
96
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

We compute the number of rhombus tilings of a hexagon with side lengths a, b, c, a, b, c which contain the central rhombus and the number of rhombus tilings of a hexagon with side lengths a, b, c, a, b, c which contain the ``almost central'' rhombus above the centre.

📜 SIMILAR VOLUMES

Rhombus Tilings of a Hexagon with Three
Rhombus Tilings of a Hexagon with Three Fixed Border Tiles
✍ Theresia Eisenkölbl 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 195 KB

We compute the number of rhombus tilings of a hexagon with sides a, b, c, a, b, c with three fixed tiles touching the border. The particular case a=b=c solves a problem posed by Propp. Our result can also be viewed as the enumeration of plane partitions having a rows and b columns, with largest entr

The Number of Rhombus Tilings of a “Punc
The Number of Rhombus Tilings of a “Punctured” Hexagon and the Minor Summation Formula
✍ S Okada; C Krattenthaler 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 403 KB

We compute the number of all rhombus tilings of a hexagon with sides a, b q 1, c, a q 1, b, c q 1, of which the central triangle is removed, provided a, b, c , where B ␣ , ␤, ␥ is the number of plane partitions inside the ␣ = ␤ = ␥ box. The proof uses nonintersecting lattice paths and a new identit