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- W2963140391 abstract "MacMahon's classical theorem on boxed plane partitions states that the generating function of the plane partitions fitting in an a×b×c box is equal toHq(a)Hq(b)Hq(c)Hq(a+b+c)Hq(a+b)Hq(b+c)Hq(c+a), where Hq(n):=[0]q!⋅[1]q!…[n−1]q! and [n]q!:=∏i=1n(1+q+q2+…+qi−1). By viewing a boxed plane partition as a lozenge tiling of a semi-regular hexagon, MacMahon's theorem yields a natural q-enumeration of lozenge tilings of the hexagon. However, such q-enumerations do not appear often in the domain of enumeration of lozenge tilings. In this paper, we consider a new q-enumeration of lozenge tilings of a hexagon with three bowtie-shaped regions removed from three non-consecutive sides. The unweighted version of the result generalizes a problem posed by James Propp on enumeration of lozenge tilings of a hexagon of side-lengths 2n, 2n+3, 2n, 2n+3, 2n, 2n+3 (in cyclic order) with the central unit triangles on the (2n+3)-sides removed. Moreover, our result also implies a q-enumeration of boxed plane partitions with certain constraints." @default.
- W2963140391 created "2019-07-30" @default.
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- W2963140391 date "2017-01-01" @default.
- W2963140391 modified "2023-09-25" @default.
- W2963140391 title "A q-enumeration of lozenge tilings of a hexagon with three dents" @default.
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- W2963140391 doi "https://doi.org/10.1016/j.aam.2016.07.002" @default.
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