• Corpus ID: 119647383

# One-Dimensional Packing: Maximality Implies Rationality

@article{Propp2017OneDimensionalPM,
title={One-Dimensional Packing: Maximality Implies Rationality},
author={James Gary Propp},
journal={arXiv: Combinatorics},
year={2017}
}
• J. Propp
• Published 28 April 2017
• Mathematics
• arXiv: Combinatorics
Every set of natural numbers determines a generating function convergent for $q \in (-1,1)$ whose behavior as $q \rightarrow 1^-$ determines a germ. These germs admit a natural partial ordering that can be used to compare sizes of sets of natural numbers in a manner that generalizes both cardinality of finite sets and density of infinite sets. For any finite set $D$ of positive integers, call a set $S$ "$D$-avoiding" if no two elements of $S$ differ by an element of $D$. It is shown that any \$D…

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