In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers π i , j {\displaystyle \pi _{i,j}}...

In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive...

function Partition function (number theory) Pentagonal number theorem Plane partition Quotition and partition Rank of a partition Crank of a partition Solid...

In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation...

Partition of unity, of a topological space Plane partition, in mathematics and especially combinatorics Graph partition, the reduction of a graph to a smaller...

for the number of reverse plane partitions of a given shape. If λ is a partition of some integer p, a reverse plane partition of n with shape λ is obtained...

obtaining asymptotic formulae. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to...

number 1902 = number of symmetric plane partitions of 27 1903 = generalized Catalan number 1904 = number of flat partitions of 43 1905 = Fermat pseudoprime...

the partitioning planes are frequently chosen to coincide with the planes defined by polygons in the scene. The specific choice of partitioning plane and...

solid partitions are natural generalizations of integer partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition of n {\displaystyle...

material element Hogel - holographic element Pixel – picture element Plane partition Resel – resolution element Sparse voxel octree Texel – texture element...

tree. Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region...

decreasing entries have been considered, notably, in the theory of plane partitions. There are also generalizations such as domino tableaux or ribbon tableaux...

the perimeter. A partition wall is a usually thin wall that is used to separate or divide a room, primarily a pre-existing one. Partition walls are usually...

introduced by Bender & Knuth (1972, pp. 46–47) in their study of plane partitions. The Bender–Knuth involutions σ k {\displaystyle \sigma _{k}} are defined...

Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS...

classes of lines. The lines in any parallel class form a partition the points of the affine plane. Each of the n + 1 lines that pass through a single point...

Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS...

Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS...

the OEIS) corresponds to cyclically symmetric transpose complement plane partitions and for n {\displaystyle n} odd, (sequence A005156 in the OEIS), these...

cube can be partitioned by exactly n planes. The cake number is so called because one may imagine each partition of the cube by a plane as a slice made...

Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS...

graphical forest partitions of 30, since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane. 509 is: a...

Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS...

groups, the statistics of plane partitions, and the quantum cohomology of the Hilbert scheme of points in the complex plane. Much of his work on Hilbert...

Airborne Operations Center" (NAOC) and has been nicknamed the "Doomsday plane". Two of the original 747-200 airframes were originally planned to be commercial...

polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number...

and Rumsey, Howard, Jr., Alternating sign matrices and descending plane partitions, Journal of Combinatorial Theory, Series A, 34 (1983), 340-359. Robbins...

geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs...

graph of line segments in the plane. The planar separator theorem states that every n-vertex planar graph can be partitioned into two subgraphs of size at...