The main aim of this paper is to describe a procedure for calculating the number of cubes that have coordinates in the set {0, 1, . . . , n}. For this purpose we continue and, at the same time, revise some of the work begun in a sequence of papers about equilateral triangles and regular tetrahedra all having integer coordinates for their vertices. We adapt the code that was included in a paper by the first author and was used to calculate the number of regular tetrahedra with vertices in {0, 1, . . . , n}3. The idea is based on the theoretical results obtained by the first author with A. Markov. We then extend the sequence A098928 in the Online Encyclopedia of Integer Sequences to the first one hundred terms
Combinatorics is the field of mathematics studying the combination and permutation of sets of elemen...
This article answers an important theoretical question: How many different subdivisions of the hexah...
Abstract. Recently there has been tremendous interest in counting the number of integral points in n...
The main aim of this paper is to describe a procedure for calculating the number of cubes that have ...
AbstractTextIn this note we characterize all regular tetrahedra whose vertices in R3 have integer co...
In this paper we introduce theoretical arguments for constructing a procedure that allows one to fin...
In this paper we describe a procedure for calculating the number of regular octahedra, RO(n), which ...
In this note we characterize all regular tetrahedra whose vertices in R 3 have integer coordinates. ...
Abstract. We describe a procedure of counting all equilateral triangles in the three dimensional spa...
AbstractTextExtending previous results on a characterization of all equilateral triangle in space ha...
AbstractWe consider simplices in Rmwith lattice point vertices, no other boundary lattice points and...
Let M be a finite set of random uniformly distributed points lying in a unit cube. Every four points...
This paper is about 0/1-triangles, which are the simplest nontrivial examples of 0/1-polytopes: conv...
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) a...
summary:This paper is about $0/1$-triangles, which are the simplest nontrivial examples of $0/1$-pol...
Combinatorics is the field of mathematics studying the combination and permutation of sets of elemen...
This article answers an important theoretical question: How many different subdivisions of the hexah...
Abstract. Recently there has been tremendous interest in counting the number of integral points in n...
The main aim of this paper is to describe a procedure for calculating the number of cubes that have ...
AbstractTextIn this note we characterize all regular tetrahedra whose vertices in R3 have integer co...
In this paper we introduce theoretical arguments for constructing a procedure that allows one to fin...
In this paper we describe a procedure for calculating the number of regular octahedra, RO(n), which ...
In this note we characterize all regular tetrahedra whose vertices in R 3 have integer coordinates. ...
Abstract. We describe a procedure of counting all equilateral triangles in the three dimensional spa...
AbstractTextExtending previous results on a characterization of all equilateral triangle in space ha...
AbstractWe consider simplices in Rmwith lattice point vertices, no other boundary lattice points and...
Let M be a finite set of random uniformly distributed points lying in a unit cube. Every four points...
This paper is about 0/1-triangles, which are the simplest nontrivial examples of 0/1-polytopes: conv...
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) a...
summary:This paper is about $0/1$-triangles, which are the simplest nontrivial examples of $0/1$-pol...
Combinatorics is the field of mathematics studying the combination and permutation of sets of elemen...
This article answers an important theoretical question: How many different subdivisions of the hexah...
Abstract. Recently there has been tremendous interest in counting the number of integral points in n...