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A Pick-type theorem for halfway-lattice polygons
Abstract
Given a polygon in the plane with vertices on lattice points, Pick's theorem expresses its area A in terms of the number I of lattice points in its interior and the number B of lattice points in its boundary: A = I + B/2 - 1. We consider polygons in the plane whose edges are halfway between lattice points. For such a polygon that is also unimodular, we express its area A in terms of the number I of lattice points in its interior and the number V of its vertices: A = I - V/8 + 1/2 .
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BibTeX
@misc{chu2026picktype,
title = {{A Pick-type theorem for halfway-lattice polygons}},
author = {Charlene Chu and Yael Karshon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00696},
eprint = {2610.00696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00696},
}
RIS
TY - UNPB
TI - A Pick-type theorem for halfway-lattice polygons
AU - Charlene Chu
AU - Yael Karshon
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00696
UR - https://arxiv.org/abs/2610.00696
AB - Given a polygon in the plane with vertices on lattice points, Pick's theorem expresses its area A in terms of the number I of lattice points in its interior and the number B of lattice points in its boundary: A = I + B/2 - 1. We consider polygons in the plane whose edges are halfway between lattice points. For such a polygon that is also unimodular, we express its area A in terms of the number I of lattice points in its interior and the number V of its vertices: A = I - V/8 + 1/2 .
ER -