PreprintCC BY 4.0arXiv
A proof of the Holmes-Holroyd-Ramirez cyclic-product conjecture
Abstract
We prove the cyclic-product conjecture of Holmes, Holroyd and Ramírez: among all circular arrangements of a decreasing positive sequence, the circular-symmetric ``greedy'' arrangement maximises every consecutive cyclic product sum Pr.
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BibTeX
@misc{ivanisvili2026proof,
title = {{A proof of the Holmes-Holroyd-Ramirez cyclic-product conjecture}},
author = {Paata Ivanisvili and Shengtong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27843},
eprint = {2609.27843},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27843},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A proof of the Holmes-Holroyd-Ramirez cyclic-product conjecture
AU - Paata Ivanisvili
AU - Shengtong Zhang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27843
UR - https://arxiv.org/abs/2609.27843
AB - We prove the cyclic-product conjecture of Holmes, Holroyd and Ramírez: among all circular arrangements of a decreasing positive sequence, the circular-symmetric ``greedy'' arrangement maximises every consecutive cyclic product sum P_r.
ER -