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Enumeration of Lozenge Tilings of Hexagons with a Central Triangular Hole

✍ Scribed by M. Ciucu; T. Eisenkölbl; C. Krattenthaler; D. Zare

Book ID
102970641
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
789 KB
Volume
95
Category
Article
ISSN
0097-3165

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✦ Synopsis

We deal with unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a, b+m, c, a+m, b, c+m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (&1)-enumeration of these lozenge tilings. In the case that a=b=c, we also provide closed formulas for certain weighted enumerations of those lozenge tilings that are cyclically symmetric. For m=0, the latter formulas specialize to statements about weighted enumerations of cyclically

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