PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{schonfelder202613phenomenon,
title = {{The 1/3-phenomenon of placement probabilities of tilings in the semiregular hexagon}},
author = {Marcus Schönfelder},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10449},
eprint = {2607.10449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The 1/3-phenomenon of placement probabilities of tilings in the semiregular hexagon
AU - Marcus Schönfelder
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.10449
UR - https://arxiv.org/abs/2607.10449
AB - 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.
ER -