Rhombus Tilings of a Hexagon with Two Triangles Missing on the Symmetry Axis

We compute the number of rhombus tilings of a hexagon with sides n, n, N, n, n, N, where two triangles on the symmetry axis touching in one vertex are removed. The case of the common vertex being the center of the hexagon solves a problem posed by Propp.Comment: 16 pages, AmS-LaTeX, uses TeXDra

Lozenge tilings of a hexagon with a horizontal intrusion

Motivated by the conjecture posed by Fulmek and Krattenthaler, we provide product formulas for the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion. As a direct corollary, we obtain the product formula for the number of boxed plane partitions with a certain restriction. We also investigate the asymptotic behavior of the ratio between the number of lozenge tilings of a semiregular hexagon containing a horizontal intrusion and that of a semiregular hexagon without an intrusion.Comment: 23 pages, 15 figures, change the title, fix some typos, rewrite some parts, and change/add some figures. Any comments would be appreciate