Subsets ofFq[x]free of 3-term geometric progressions
| Autor: | Eva Fourakis, Steven J. Miller, Megumi Asada, Sarah Manski, Gwyneth Moreland, Nathan McNew |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Applied Mathematics Ramsey theory Problems involving arithmetic progressions General Engineering Structure (category theory) 010103 numerical & computational mathematics 0102 computer and information sciences Algebraic number field Term (logic) 01 natural sciences Theoretical Computer Science Geometric progression Set (abstract data type) Combinatorics 010201 computation theory & mathematics 0101 mathematics Mathematics |
| Zdroj: | Finite Fields and Their Applications. 44:135-147 |
| ISSN: | 1071-5797 |
| DOI: | 10.1016/j.ffa.2016.10.002 |
| Popis: | Several recent papers have considered the Ramsey-theoretic problem of how large a subset of integers can be without containing any 3-term geometric progressions. This problem has also recently been generalized to number fields, determining bounds on the greatest possible density of ideals avoiding geometric progressions. We study the analogous problem over F q x , first constructing a set greedily which avoids these progressions and calculating its density, and then considering bounds on the upper density of subsets of F q x which avoid 3-term geometric progressions. This new setting gives us a parameter q to vary and study how our bounds converge to 1 as it changes, and positive characteristic introduces some extra combinatorial structure that increases the tractability of common questions in this area. |
| Databáze: | OpenAIRE |
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