Pregled bibliografske jedinice broj: 1094874
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
Boxes, extended boxes, and sets of positive upper density in the Euclidean space // Mathematical proceedings of the Cambridge Philosophical Society, 171 (2021), 3; 481-501 doi:10.1017/S0305004120000316 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 1094874 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
Autori
Durcik, Polona ; Kovač, Vjekoslav
Izvornik
Mathematical proceedings of the Cambridge Philosophical Society (0305-0041) 171
(2021), 3;
481-501
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
density ; configuration ; arithmetic progression
Sažetak
We prove that sets with positive upper Banach density in sufficiently large dimensions contain congruent copies of all sufficiently large dilates of three specific higher-dimensional patterns. These patterns are: 2^n vertices of a fixed n-dimensional rectangular box, the same vertices extended with n points completing three-term arithmetic progressions, and the same vertices extended with n points completing three-point corners. Our results provide common generalizations of several Euclidean density theorems from the literature.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-UIP-2017-05-4129 - Multilinearna i nelinearna harmonijska analiza i primjene (MUNHANAP) (Kovač, Vjekoslav, HRZZ ) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
Profili:
Vjekoslav Kovač
(autor)
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
