PreprintCC BY 4.0arXiv
Functions determining few direction: the final missing case
Abstract
By results of Blokhuis, Ball, Brouwer, Storme and Szőnyi, and of Ball, if a function f: 𝔽q→𝔽q determines fewer than (q+3)/2 directions, then f−f(0) is linear over a subfield of 𝔽q, except possibly when q is even and f determines exactly q/2+1 directions. We settle this case: f−f(0) is then additive. Hence every small minimal blocking set of Rédei type in PG(2,q) is linear.
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BibTeX
@misc{sziklai2026functions,
title = {{Functions determining few direction: the final missing case}},
author = {Peter Sziklai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28002},
eprint = {2610.28002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Functions determining few direction: the final missing case
AU - Peter Sziklai
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28002
UR - https://arxiv.org/abs/2610.28002
AB - By results of Blokhuis, Ball, Brouwer, Storme and Szőnyi, and of Ball, if a function f: 𝔽_q→𝔽_q determines fewer than (q+3)/2 directions, then f−f(0) is linear over a subfield of 𝔽_q, except possibly when q is even and f determines exactly q/2+1 directions. We settle this case: f−f(0) is then additive. Hence every small minimal blocking set of Rédei type in PG(2,q) is linear.
ER -