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Hypercube eigenfunctions with two strong nodal domains
Abstract
Bıyıko{\u g}lu, Hordijk, Leydold, Pisanski, and Stadler conjectured that, for every n≥3 and 1≤ i≤ n−2, the hypercube Qn admits a Laplacian eigenfunction with eigenvalue 2i and exactly two strong nodal domains. In this paper, we confirm this conjecture.
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BibTeX
@misc{he2026hypercube,
title = {{Hypercube eigenfunctions with two strong nodal domains}},
author = {Yize He and Qinghong Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21978},
eprint = {2609.21978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21978},
}
RIS
TY - UNPB
TI - Hypercube eigenfunctions with two strong nodal domains
AU - Yize He
AU - Qinghong Zhao
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21978
UR - https://arxiv.org/abs/2609.21978
AB - Bıyıko{\u g}lu, Hordijk, Leydold, Pisanski, and Stadler conjectured that, for every n≥3 and 1≤ i≤ n−2, the hypercube Q_n admits a Laplacian eigenfunction with eigenvalue 2i and exactly two strong nodal domains. In this paper, we confirm this conjecture.
ER -