Boxes, extended boxes, and sets of positive upper density in the Euclidean space (CROSBI ID 286412)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Durcik, Polona ; Kovač, Vjekoslav
engleski
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
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.
density ; configuration ; arithmetic progression
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
Podaci o izdanju
171 (3)
2021.
481-501
objavljeno
0305-0041
1469-8064
10.1017/S0305004120000316