• Corpus ID: 119647383

One-Dimensional Packing: Maximality Implies Rationality

  title={One-Dimensional Packing: Maximality Implies Rationality},
  author={James Gary Propp},
  journal={arXiv: Combinatorics},
  • 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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