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- Title
GERM ORDER FOR ONE-DIMENSIONAL PACKINGS.
- Authors
ABRAMS, AARON; LANDAU, HENRY; LANDAU, ZEPH; POMMERSHEIM, JAMIE; PROPP, JAMES; RUSSELL, ALEXANDER
- Abstract
Every set of natural numbers determines a generating function convergent for q 2 (2, 1) whose behavior as q 1 determines a germ. These germs admit a natural partial ordering that can be used to compare 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. We study the problem of determining, for fixed D, all Davoiding sets that are maximal in the germ order. In many cases, we can show that there is exactly one such set. We apply this to the study of one-dimensional packing problems.
- Subjects
PACKING problem (Mathematics); NATURAL numbers; GENERATING functions; INTEGERS; CARDINAL numbers; SET theory
- Publication
Online Journal of Analytic Combinatorics, 2021, Issue 16, p1
- ISSN
1931-3365
- Publication type
Article