Geometric lattice information

matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular lattice without the...

point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified...

structure and frustration in spin; the second is the geometrical frustration with an ordered lattice structure and frustration of spin. The frustration...

In physics, the reciprocal lattice emerges from the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in...

The atoms in a solid are bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice), or irregularly...

physical world and its model provided by Euclidean geometry; presently a geometric space, or simply a space is a mathematical structure on which some geometry...

partially ordered sets, a finite simple matroid is equivalent to a geometric lattice. Matroid theory borrows extensively from the terms used in both linear...

is itself a partial order relation, which makes the collection a geometric lattice. Given any set X , {\displaystyle X,} an equivalence relation over...

grove accompanied by children. Cantilevered brackets in well shaft Geometric lattice patterns and designs resembling Patola textile designs There are gradually...

which might seem more natural but would not yield a geometric (semi)lattice.) When L(A) is a lattice, the matroid of A, written M(A), has A for its ground...

hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper...

monoclinic and triclinic. Bravais lattices, also referred to as space lattices, describe the geometric arrangement of the lattice points, and therefore the translational...

(with the simple, two circle form named vesica piscis) or on the square lattice pattern of points. Patterns of seven overlapping circles appear in historical...

element of the lattice of subgroups. Richard Stanley noticed in the 1970s that certain geometric lattices, such as the partition lattice, obeyed similar...

it forms a lattice, and more specifically (for partitions of a finite set) it is a geometric and supersolvable lattice. The partition lattice of a 4-element...

finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of...

is called a geometric lattice and corresponds to a matroid of finite rank. Semimodular lattices are also known as upper semimodular lattices; the dual notion...

lattice is geometric. (def) 25. A geometric lattice is semi-modular. 26. A semi-modular lattice is atomic.[disputed – discuss] 27. An atomic lattice is a lattice...

instead of fields. A Dowling lattice is the geometric lattice of flats associated with a Dowling geometry. The lattice and the geometry are mathematically...

random packing of equal spheres generally has a density around 63.5%. A lattice arrangement (commonly called a regular arrangement) is one in which the...

The oblique lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p2. The primitive...

kagome lattice arrangement of atoms in their crystal structure. These minerals display novel physical properties connected with geometrically frustrated...

the face-centered cubic Bravais lattice. The lattice describes the repeat pattern; for diamond cubic crystals this lattice is "decorated" with a motif of...

Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that...

groups: For each geometric class, the possible arithmetic classes are None: no reflection lines Along: reflection lines along lattice directions Between:...

Geometric phase analysis is a method of digital signal processing used to determine crystallographic quantities such as d-spacing or strain from high-resolution...

girders of steel bolted together in a geometric lattice. The truncated tetrahedra were interconnected with lattice steel platforms. All of these buildings...