PreprintCC BY 4.0arXiv
A linear gap for the maximal cp-rank
Abstract
We prove that the maximal cp-rank pn satisfies pn≥ n(n−3)/2 for odd n≥5 and pn≥ n(n−3)/2−1 for even n≥6. Together with the known upper bound pn≤binomn+12−4, this gives pn=n2/2+O(n).
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BibTeX
@misc{lavi2026linear,
title = {{A linear gap for the maximal cp-rank}},
author = {Yair Lavi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02289},
eprint = {2610.02289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02289},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A linear gap for the maximal cp-rank
AU - Yair Lavi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02289
UR - https://arxiv.org/abs/2610.02289
AB - We prove that the maximal cp-rank p_n satisfies p_n≥ n(n−3)/2 for odd n≥5 and p_n≥ n(n−3)/2−1 for even n≥6. Together with the known upper bound p_n≤binomn+12−4, this gives p_n=n^2/2+O(n).
ER -