mathematics, the n-dimensional integer lattice (or cubic lattice), denoted ⁠ Z n {\displaystyle \mathbb {Z} ^{n}} ⁠, is the lattice in the Euclidean space ⁠...

based on the integer lattice, hexagonal tiling and E8 lattice, respectively. It has no root system and in fact is the first unimodular lattice with no roots...

uniquely expressed as an integer combination of finitely many basis elements. For instance, the two-dimensional integer lattice forms a free abelian group...

lengths of line segments between pairs of points in the two-dimensional integer lattice. The number of representable numbers in the range from 0 to any number...

factorization of a positive integer Complex integer Hyperinteger Integer complexity Integer lattice Integer part Integer sequence Integer-valued function Mathematical...

In combinatorics, a lattice path L in the d-dimensional integer lattice ⁠ Z d {\displaystyle \mathbb {Z} ^{d}} ⁠ of length k with steps in the set S,...

)n} with an integer n {\displaystyle n} ) at every direct lattice vertex. One heuristic approach to constructing the reciprocal lattice in three dimensions...

the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as ⁠...

mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This...

The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex...

either is an integer or a half-integer (has a denominator of 2). If the lattice triangle has integer sides then it is Heronian with integer area. Furthermore...

{\sqrt {3}}} ⁠ apart in the integer lattice; the edges of the diamond structure lie along the body diagonals of the integer grid cubes. This structure...

set of integer numbers. For a lattice Λ, Minkowski's theorem relates the number d(Λ) (the volume of a fundamental parallelepiped of the lattice) and the...

the Gaussian integers constitute the 2-dimensional integer lattice. The conjugate of a Gaussian integer a + bi is the Gaussian integer a − bi. The norm...

} of non-negative integers into a partially ordered set that is a complete distributive lattice. The largest element of this lattice is 0 and the smallest...

combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed...

mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius...

In mathematics, Young's lattice is a lattice that is formed by all integer partitions. It is named after Alfred Young, who, in a series of papers On quantitative...

includes at least ⌈ A ⌉ {\displaystyle \lceil A\rceil } points of the integer lattice. Equivalently, every bounded set of area A {\displaystyle A} contains...

"lattice" is suggested by the form of the Hasse diagram depicting it. Pic. 2: Lattice of integer divisors of 60, ordered by "divides". Pic. 3: Lattice...

provides the largest constant-width shape avoiding the points of an integer lattice, and is closely related to the shape of the quadrilateral maximizing...

are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special...

26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved...

Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd integers; a mixture of integers and half-integers...

In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability...

certain average-case lattice problem, known as short integer solutions (SIS), is at least as hard to solve as a worst-case lattice problem. She then showed...

Binary images can be interpreted as subsets of the two-dimensional integer lattice Z2; the field of morphological image processing was largely inspired...

wazir form a square lattice graph. Lattice path Pick's theorem Integer triangles in a 2D lattice Regular graph Weisstein, Eric W. "Lattice graph". MathWorld...

of the Laves graph uses one out of every eight of the points in the integer lattice as its points, and connects all pairs of these points that are nearest...

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of...