𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Number of Rhombus Tilings of a “Punctured” Hexagon and the Minor Summation Formula

✍ Scribed by S Okada; C Krattenthaler

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
403 KB
Volume
21
Category
Article
ISSN
0196-8858

No coin nor oath required. For personal study only.

✦ Synopsis

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 identity for Schur functions, which is proved by w means of the minor summation formula of Ishikawa and Wakayama. Proc. Japan Ž .

x Acad. Ser. A 71 1995 , 54᎐57 . A symmetric generalization of this identity is stated as a conjecture.

📜 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 Centered Lozenge Tilings o
The Number of Centered Lozenge Tilings of a Symmetric Hexagon
✍ M Ciucu; C Krattenthaler 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 257 KB

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

Bass Numbers in the Graded Case, a-Invar
Bass Numbers in the Graded Case, a-Invariant Formulas, and an Analogue of Faltings' Annihilator Theorem
✍ Rodney Y Sharp 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 180 KB

Let R = n≥0 R n be a positively graded commutative Noetherian ring. A graded R-module is called \*indecomposable (respectively \*injective) if it is indecomposable (respectively injective) in the category of graded R-modules. Let M = n∈ M n be a finitely generated graded R-module. The first main re