Tilings of hexagons with a removed triad of bowties

In this paper we consider arbitrary hexagons on the triangular lattice with three bowtie-shaped holes, whose centers form an equilateral triangle. The number of lozenge tilings such general regions is not expected — and indeed given by a simple product formula. However, when considering certain natural normalized counterpart R any region R, prove that ratio between simple, conceptual Several seemingly unrelated previous results from literature including Lai's formula for dents Ciucu Krattenthaler's removed shamrock follow as immediate special cases our result.