𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Rhombus Tilings of a Hexagon with Three Fixed Border Tiles

✍ Scribed by Theresia Eisenkölbl

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
195 KB
Volume
88
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 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 entry c, with a given number of entries equal to c in the first row, a given number of entries equal to 0 in the last column, and a given bottom-left entry.

📜 SIMILAR VOLUMES

Enumeration of Rhombus Tilings of a Hexa
Enumeration of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus in the Centre
✍ Ilse Fischer 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 418 KB

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.

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