Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings of a hexagon with ''maximal staircases'' removed from some of its vertices. The case of one vertex c
Enumeration of Lozenge Tilings of Punctured Hexagons
β Scribed by Mihai Ciucu
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 232 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0097-3165
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β¦ Synopsis
We present a combinatorial solution to the problem of determining the number of lozenge tilings of a hexagon with sides a, b+1, b, a+1, b, b+1, with the central unit triangle removed. For a=b, this settles an open problem posed by Propp [7].
π SIMILAR VOLUMES
Propp conjectured that the number of lozenge tilings of a semiregular hexagon of sides 2n&1, 2n&1, and 2n which contain the central unit rhombus is precisely one third of the total number of lozenge tilings. Motivated by this, we consider the more general situation of a semiregular hexagon of sides
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 β£ , β€, β₯ is the number of plane partitions inside the β£ = β€ = β₯ box. The proof uses nonintersecting lattice paths and a new identit
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.
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