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

geometric lattice is an infinite, regular array of vertices (points) in space, which can be modelled vectorially as a Bravais lattice. Some lattices may...

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...

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...

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

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...

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

discrete sites on a geometric lattice. A perfect crystal consists of a regular and periodic geometric lattice. The perfect lattice has translation symmetry...

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

this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. As a group (dropping its geometric structure)...

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...

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

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

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

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

amounts to the usual geometric notion of a lattice as a periodic subset of points, and both the algebraic structure of lattices and the geometry of the...

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...

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...

An overlapping circles grid is a geometric pattern of repeating, overlapping circles of an equal radius in two-dimensional space. Commonly, designs are...

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...

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...

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

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...

Rainbow lattice sunstone, also known as rainbow lattice, is a type of orthoclase feldspar that exhibits a rare combination of aventurescence, adularescence...

Since the lattices of flats of matroids are exactly the geometric lattices, this implies that the lattice of partitions is also geometric. The graphic...

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

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

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

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

exponential (geometric integral), from which Wilson loop values can be calculated for closed paths. The Yang–Mills action is written on the lattice using Wilson...