2018/03/07 by Tri Lai, Lai, Tri · 2 citations
Mathematics · #05A15 #05B45 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:05B45
paper · pdf · doi:10.48550/arxiv.1803.02792
Version 6: 52 pages. Version 6 is roughly the first half of Version 5, which also contained the material that is now arXiv:1905.07119. Version 6 contains minor expository changes
arxiv created 2019/05/20 · arxiv updated 2019/05/21
Ciucu showed that the number of lozenge tilings of a hexagon in which a chain of equilateral triangles of alternating orientations, called a `fern', has been removed in the center is given by a simple product formula (Adv. Math. 2017). In this paper, we present a multi-parameter generalization of this work by giving an explicit tiling enumeration for a hexagon with three ferns removed, besides the middle fern located in the center as in Ciucu's region, we remove two additional ferns from two sides of the hexagon. Our result also implies a counterpart of MacMahon's classical formula of boxed plane partitions, corresponding the exterior of the union of three disjoint concave polygons obtained by turning 120 degrees after drawing each side.