The 1/3-phenomenon of placement probabilities of tilings in the semiregular hexagon

Abstract

We prove Krattenthaler's conjecture from 2001 about the $1/3$-phenomenon for lozenge tilings of semiregular hexagons. In a first step we reduce the problem to the case of regular hexagons. In a second step we further reduce the question to a special case already covered in the literature. This is achieved by vast application of the celebrated Zeilberger Algorithm and the Holonomic Ansatz.