PreprintCC BY 4.0arXiv
A Mean Value Property in Powers of the Natural Square
Abstract
Let n≥ 1 be an odd integer, set m=(n−1)/2 and let M be an n× n matrix whose coefficients are of the form Mi,j=aij+bi+cj+d where 0≤ i,j≤ n−1. Then we prove that for all squares centered at the central coefficient Mm,m, the mean value of the square equals Mm,m.
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BibTeX
@misc{jolissaint2026mean,
title = {{A Mean Value Property in Powers of the Natural Square}},
author = {Paul Jolissaint and Kenichi Takemura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05551},
eprint = {2609.05551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05551},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Mean Value Property in Powers of the Natural Square
AU - Paul Jolissaint
AU - Kenichi Takemura
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.05551
UR - https://arxiv.org/abs/2609.05551
AB - Let n≥ 1 be an odd integer, set m=(n−1)/2 and let M be an n× n matrix whose coefficients are of the form M_i,j=aij+bi+cj+d where 0≤ i,j≤ n−1. Then we prove that for all squares centered at the central coefficient M_m,m, the mean value of the square equals M_m,m.
ER -