KAKEYA SETS OVER NON‐ARCHIMEDEAN LOCAL RINGS

Autor:	Márton Hablicsek, Evan P. Dummit
Rok vydání:	2013
Předmět:	Combinatorics 05B30 (Primary) 51E20 (Secondary) General Mathematics Kakeya set FOS: Mathematics Local ring Minkowski–Bouligand dimension Mathematics - Combinatorics Combinatorics (math.CO) Measure (mathematics) Mathematics
Zdroj:	Mathematika. 59:257-266
ISSN:	2041-7942 0025-5793
DOI:	10.1112/s002557931300003x
Popis:	In a recent paper of Ellenberg, Oberlin, and Tao, the authors asked whether there are Besicovitch phenomena in F_q[[t]]^n. In this paper, we answer their question in the affirmative by explicitly constructing a Kakeya set in F_q[[t]]^n of measure 0. Furthermore, we prove that any Kakeya set in F_q[[t]]^2 or Z_p^2 is of Minkowski dimension 2. Comment: 10 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3593ac9919695bd7f9f2aa9d6c70b68 https://doi.org/10.1112/s002557931300003x Zobrazit plný text záznamu Plný text