2 citations · 2 across the 6 of their papers we have counts for
6 papers
On the characteristic and diameter of planar integral point sets
N. N. Avdeev, E. A. Lushina
A point set in Euclidean plane is called an integral point set in semi-general position if all the distances between the elements of are integers, and does not contain…
On particular examples of planar integral point sets and their classification
Nikolai Avdeev, Ekaterina Momot, Aleksandr Zvolinskiy
A planar integral point set is a set of non-collinear points in plane such that for any pair of the points the Euclidean distance between the points is integral. We discuss the cla…
The subspace is not complemented in
Nikolai Avdeev
We prove that the subspace of sequences that converge to zero is not complemented in the space of sequences that almost converge to zero. We proceed with applying the…
On particular diameter bounds for integral point sets in higher dimensions
N. N. Avdeev, R. E. Zvolinsky, E. A. Momot
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integ…
On diameter bounds for planar integral point sets in semi-general position
N. N. Avdeev
A point set in the Euclidean plane is called a planar integral point set if all the distances between the elements of are integers, and is not situated on a straight li…
On existence of integral point sets and their diameter bounds
Nikolai Avdeev
A point set in -dimensional Euclidean space is called an integral point set if all the distances between the elements of are integers, and is not situated on an $(m-…