Optimality of Kløve Arrays within the Symmetric Kløve-Mossige Class
Abstract
Rajamunicode228ki and Koivunen asked whether minimum-redundancy symmetric Klunicode248ve-Mossige arrays with contiguous sum co-arrays are always Klunicode248ve arrays. We give a computer-assisted proof that, at every fixed sensor count, every maximizing sensor set belongs to the Klunicode248ve class. The argument classifies the overlaps between a generator and its shifted reflection, then bounds the aperture of a hypothetical optimizer outside the Klunicode248ve class. Comparing these bounds with a classical Klunicode248ve construction settles all sensor counts at least 330. An exact integer certificate covers the remaining counts from 2 through 329 and matches every equality case to a Klunicode248ve array as a complete set. Consequently, optimization within the full symmetric Klunicode248ve-Mossige class reduces to the previously known search over Klunicode248ve parameters. The theorem concerns this specified class, rather than unrestricted sparse arrays or all restricted additive bases.
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BibTeX
@misc{yan2026optimality,
title = {{Optimality of Kløve Arrays within the Symmetric Kløve-Mossige Class}},
author = {Lilin Yan and Hongwei Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09239},
eprint = {2609.09239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09239},
}
RIS
TY - UNPB
TI - Optimality of Kløve Arrays within the Symmetric Kløve-Mossige Class
AU - Lilin Yan
AU - Hongwei Zhao
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09239
UR - https://arxiv.org/abs/2609.09239
AB - Rajamunicode228ki and Koivunen asked whether minimum-redundancy symmetric Klunicode248ve-Mossige arrays with contiguous sum co-arrays are always Klunicode248ve arrays. We give a computer-assisted proof that, at every fixed sensor count, every maximizing sensor set belongs to the Klunicode248ve class. The argument classifies the overlaps between a generator and its shifted reflection, then bounds the aperture of a hypothetical optimizer outside the Klunicode248ve class. Comparing these bounds with a classical Klunicode248ve construction settles all sensor counts at least 330. An exact integer certificate covers the remaining counts from 2 through 329 and matches every equality case to a Klunicode248ve array as a complete set. Consequently, optimization within the full symmetric Klunicode248ve-Mossige class reduces to the previously known search over Klunicode248ve parameters. The theorem concerns this specified class, rather than unrestricted sparse arrays or all restricted additive bases.
ER -