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The Number of Centered Lozenge Tilings of a Symmetric Hexagon

✍ Scribed by M Ciucu; C Krattenthaler

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
257 KB
Volume
86
Category
Article
ISSN
0097-3165

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✦ Synopsis

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 a, a, and b. We prove explicit formulas for the number of lozenge tilings of these hexagons containing the central unit rhombus and obtain Propp's conjecture as a corollary of our results.

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