PreprintCC BY 4.0arXiv
Prime Nullspace Matrices and Even Dominating Sets
Abstract
A non-zero m × n (0, 1)-matrix A is called a {\em nullspace matrix} if each entry $(i, j)$ of A has an even number of 1's in the set of entries consisting of $(i, j)$ and its rectilinear neighbors. These matrices correspond to even dominating sets of m × n grid graphs. We study these matrices and consider those that cannot be constructed from smaller nullspace matrices.
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BibTeX
@misc{klostermeyer2026prime,
title = {{Prime Nullspace Matrices and Even Dominating Sets}},
author = {William F. Klostermeyer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31475},
eprint = {2610.31475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31475},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prime Nullspace Matrices and Even Dominating Sets
AU - William F. Klostermeyer
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31475
UR - https://arxiv.org/abs/2610.31475
AB - A non-zero m × n (0, 1)-matrix A is called a {\em nullspace matrix} if each entry $(i, j)$ of A has an even number of 1's in the set of entries consisting of $(i, j)$ and its rectilinear neighbors. These matrices correspond to even dominating sets of m × n grid graphs. We study these matrices and consider those that cannot be constructed from smaller nullspace matrices.
ER -