PreprintCC BY 4.0arXiv
Determining the Rearrangement Number
Abstract
The rearrangement number rr is the least cardinality of a collection of permutations of ω such that every conditionally convergent real series is disrupted by some permutation in the collection. Blass, Brendle, Brian, Hamkins, Hardy, and Larson proved that max{cov(𝒩),b}≤rr≤non(ℳ) and asked whether rr=non(ℳ). We prove in ZFC that rr=non(ℳ).
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BibTeX
@misc{rodrigues2026determining,
title = {{Determining the Rearrangement Number}},
author = {Vinicius de Oliveira Rodrigues},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.18726},
eprint = {2607.18726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18726},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Determining the Rearrangement Number
AU - Vinicius de Oliveira Rodrigues
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2607.18726
UR - https://arxiv.org/abs/2607.18726
AB - The rearrangement number rr is the least cardinality of a collection of permutations of ω such that every conditionally convergent real series is disrupted by some permutation in the collection. Blass, Brendle, Brian, Hamkins, Hardy, and Larson proved that max{cov(𝒩),b}≤rr≤non(ℳ) and asked whether rr=non(ℳ). We prove in ZFC that rr=non(ℳ).
ER -