|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4624454||1631614||2017||35 صفحه PDF||سفارش دهید||دانلود رایگان|
MacMahon's classical theorem on boxed plane partitions states that the generating function of the plane partitions fitting in an a×b×ca×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):=q!⋅q!…[n−1]q!Hq(n):=q!⋅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+32n+3, 2n , 2n+32n+3, 2n , 2n+32n+3 (in cyclic order) with the central unit triangles on the (2n+3)(2n+3)-sides removed. Moreover, our result also implies a q-enumeration of boxed plane partitions with certain constraints.
Journal: Advances in Applied Mathematics - Volume 82, January 2017, Pages 23–57