Lozenge tilings of hexagons with removed core and satellites (Q6083996)

The problem of enumerating the number of lozenge tilings of hexagons with various boundary/interior conditions attached to them have been a problem of interest in enumerative combinatorics for a very long time. The paper under review continues in this tradtion by considering regions obtained from \(120^\circ\) rotationally invariant hexagons by removing a core and three equal satellite regions. The regions which results due to this, is both vertically symmetric and \(120^\circ\) rotationally invariant. The authors give a simple product formula for the number of lozenge tilings of these regions. In many cases, the original motivation of considering a certain combinatorial problem is opague. But in this paper, the authors have very helpfully guided the reader (in Section 1 itself) through their motivation of considering these regions and how they figure in the overaching program that the first author has studied since the early 2000s. The current paper describes a new method of approaching proofs of enumeration formulas of the kind presented in the paper, which allows them to generalize some known results as well. The paper is very well-written and will likely make a great impact on the field in the coming years.