The set of neighbours of a set in a point-lattice

✍ Scribed by B. Uhrin

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 454 KB
• Volume: 133
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)90032-9

✦ Synopsis

Given an n-dimensional point-lattice

A c [w" and a bounded set A c KY, the set S(A) of nonzero lattice points ueA such that A n (A + u) # f~ is called the set of neighbours of A in ,4. In the paper a disjoint decomposition of S(A) is showed which gives a representation of the cardinality N(A) of S(A) as the sum of cardinalities of the components of S(A). The resulting identity yields both sharpenings and generalizations of lower estimations for N(A) due to Groemer (1970) and Erdiis and Rogers (1964).