Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Schönfelder, Marcus
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
Award: G8590477180
OpenAlex ID: W7168258707