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Array of nonnegative integers in combinatorics
In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers π i , j {\displaystyle \pi _{i,j}}
Plane_partition
Type of plane partition
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
Voronoi_diagram
Decomposition of an integer as a sum of positive integers
partition Newton's identities Partition of a set Plane partition Polite number, defined by partitions into consecutive integers Rank of a partition,
Integer_partition
Mathematical formula for the number of Young tableaux
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
Hook_length_formula
Topics referred to by the same term
Partition of unity, of a topological space Plane partition, in mathematics and especially combinatorics Graph partition, the reduction of a graph to a smaller
Partition
Pentagonal number theorem Plane partition Solid partition Quotition and partition Rank of a partition Crank of a partition Young's lattice Bell number
List_of_partition_topics
Branch of discrete mathematics
obtaining asymptotic formulae. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to
Combinatorics
Method for recursively subdividing a space into two subsets using hyperplanes
the partitioning planes are frequently chosen to coincide with the planes defined by polygons in the scene. The specific choice of partitioning plane and
Binary_space_partitioning
solid partitions are natural generalizations of integer partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition of n {\displaystyle
Solid_partition
Element representing a value on a grid in three dimensional space
material element Hogel - holographic element Pixel – picture element Plane partition Resel – resolution element Sparse voxel octree Texel – texture element
Voxel
Mathematical model
and Rumsey, Howard Jr., Alternating sign matrices and descending plane partitions, Journal of Combinatorial Theory, Series A, 34 (1983), 340–359. Propp
Alternating_sign_matrix
Partition of the Euclidean plane
Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell
Power_diagram
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
Bender–Knuth_involution
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
1,000,000,000
Division of an entire space into ≥2 disjoint subsets
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
Space_partitioning
Vertical structure, usually solid, that defines and sometimes protects an area
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
Wall
Concept in combinatorics
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
Cake_number
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
10,000
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
20,000
Combinatorial object in representation theory
decreasing entries have been considered, notably, in the theory of plane partitions. There are also generalizations such as domino tableaux or ribbon tableaux
Young_tableau
Russian mathematician (born 1969)
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
Andrei_Okounkov
Axiomatically defined geometrical space
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
Affine plane (incidence geometry)
Affine_plane_(incidence_geometry)
Algebra in statistical mechanics
the OEIS) corresponds to cyclically symmetric transpose complement plane partitions and for n {\displaystyle n} odd, (sequence A005156 in the OEIS), these
Temperley–Lieb_algebra
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
6000_(number)
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
800_(number)
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
2000_(number)
Austrian mathematician
habilitation thesis was A polynomial method for the enumeration of plane partitions and alternating sign matrices. She worked as an assistant at Alpen-Adria-Universität
Ilse_Fischer
Smallest 3D projective space
are represented as a bijection with the 35 ways to partition a 4×4 affine space into 4 parallel planes of 4 cells each. This was described by Steven H.
PG(3,2)
British mathematician (1854–1929)
best known for his study of symmetric functions and enumeration of plane partitions; see MacMahon Master theorem. His two volume Combinatory analysis,
Percy_Alexander_MacMahon
Natural number
Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS
4000_(number)
Mathematical theory
ISSN 0195-6698. Patrias, Rebecca; Pechenik, Oliver (2020). "Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture". Forum of Mathematics
Cameron–Fon-Der-Flaass IBIS theorem
Cameron–Fon-Der-Flaass_IBIS_theorem
Graph that can be embedded in the plane
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
Planar_graph
Method of computing determinants
and Rumsey, Howard, Jr., Alternating sign matrices and descending plane partitions, Journal of Combinatorial Theory, Series A, 34 (1983), 340-359. Robbins
Dodgson_condensation
Natural number
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
500_(number)
Geometric system with a finite number of points
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
Finite_geometry
Set of basic shapes which assemble into a polygon
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
Polygon_partition
(1994). "Some hidden relations involving the ten symmetry classes of plane partitions". Journal of Combinatorial Theory, Series A. 68 (2): 372–409. doi:10
Cyclic_sieving
Polygon with an infinite number of sides
partition of the Euclidean line E1 into infinitely many equal-length segments. It generalizes the regular n-gon, which may be defined as a partition of
Apeirogon
Process of partitioning a rectilinear polygon
Guillotine partition is the process of partitioning a rectilinear polygon, possibly containing some holes, into rectangles, using only guillotine-cuts
Guillotine_partition
Algebraic encoding of graph connectivity
other sciences such as the Jones polynomial from knot theory and the partition functions of the Potts model from statistical physics. It is also the
Tutte_polynomial
points in the same partition set are joined by a line. These sets are the analogs of classes of parallel lines in an affine plane, and some authors refer
Truncated_projective_plane
Smallest convex set containing a given set
convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band
Convex_hull
German mathematician and computer scientist
product formula for the orbit generating function of totally symmetric plane partitions, which was formulated by George Andrews and David Robbins in the early
Manuel_Kauers
Counts tuples of non-intersecting lattice paths
Gessel, Ira M.; Viennot, Xavier G. (1989), Determinants, Paths and Plane Partitions (PDF), archived from the original (PDF) on 2017-04-17 Lindström, Bernt
Lindström–Gessel–Viennot lemma
Lindström–Gessel–Viennot_lemma
Certain parallelograms occurring in a gnomon have areas of equal size
lines you have three planes through P {\displaystyle P} , each parallel to the faces of the parallelepiped. The three planes partition the parallelepiped
Theorem_of_the_gnomon
Indian military officer and ambassador (1907–1990)
Army General Officer who was known for being in charge of stopping the Partition Riots in both corners of India; Punjab and Bengal. He stopped riots and
Mohindar_Singh_Chopra
Compact non-orientable two-dimensional manifold
In mathematics, the real projective plane, denoted R P 2 {\displaystyle \mathbf {RP} ^{2}} or P 2 {\displaystyle \mathbb {P} _{2}} , is a two-dimensional
Real_projective_plane
Theorem in geometry about convex sets
example, in the case d = 2, any set of four points in the Euclidean plane can be partitioned in one of two ways. It may form a triple and a singleton, where
Radon's_theorem
Public holiday celebrated on 15 August
coincided with the partition of India, in which British India was divided into the Dominions of India and Pakistan; the partition was accompanied by violent
Independence_Day_(India)
tree's nodes. Each inner node's split plane is positioned on a grid plane of the underlying grid, partitioning the node's grid into two subgrids. The
Implicit_k-d_tree
Russian physicist and mathematician
combinatorics, alternating sign matrices, domino tiling, Young diagrams and plane partitions. In the same paper the determinant formula was proved for the square
Vladimir_Korepin
On partitions into intersecting convex hulls
the partition is unique. The case r = 3 {\displaystyle r=3} and d = 2 {\displaystyle d=2} states that any seven points in the plane may be partitioned into
Tverberg's_theorem
Sum of directed areas in exterior algebra
are not unique, instead every plane is orthogonal to all the vectors in its Hodge dual space. This can be used to partition the bivectors into two 'halves'
Bivector
German mathematician and computer scientist
product formula for the orbit generating function of totally symmetric plane partitions, which was formulated by George Andrews and David Robbins in the early
Christoph_Koutschan
Covering by shapes without overlaps or gaps
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Tessellation
Mathematical ranking of a set
relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order
Weak_ordering
One of several theorems in different areas of mathematics
positive integer c, there exists a positive integer S, such that for every partition of the integers { 1 , … , S } {\displaystyle \{1,\ldots ,S\}} into c parts
Schur's_theorem
First phase of the 1947–1949 Palestine war
adopted a resolution on 29 November 1947 recommending the adoption of the Partition Plan for Palestine. During the civil war, Palestine's Jewish and Arab
1947–1948 civil war in Mandatory Palestine
1947–1948_civil_war_in_Mandatory_Palestine
Approach to network management
forwarding process of network packets (data plane) from the routing process (control plane). The control plane consists of one or more controllers, which
Software-defined_networking
Concept in geometry
S2CID 117958873 Reading, Nathan (2010), "Noncrossing Partitions, Clusters and the Coxeter Plane", Séminaire Lotharingien de Combinatoire, B63b: 32 Bernšteĭn
Coxeter_element
Shape with three sides
always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge
Triangle
Distribution of strain experienced by a geological mass by type and intensity
analyzing how and why strain is partitioned: anisotropy such as preexisting structures, compositional layering, or cleavage planes. Isotropic lines "separate
Strain_partitioning
Size of a two-dimensional surface
Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface
Area
Separation of North and South Korea
The division of Korea or the partition of Korea began at the end of World War II on 2 September 1945, with the establishment of a Soviet occupation zone
Division_of_Korea
Movement to end British rule in India
radical approach towards self-rule. This began with protests against the Partition of Bengal (1905), which exposed the limits of the moderate leaders' reformist
Indian_independence_movement
Model in statistical mechanics
{\displaystyle T} and the Boltzmann constant k {\displaystyle k} , the partition function Z N ( K ≡ β J , L ≡ β J ∗ ) = ∑ { σ } exp ( K ∑ ⟨ i j ⟩ H σ
Square_lattice_Ising_model
Multidimensional search tree for points in k dimensional space
computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional
K-d_tree
Statistical mechanics model for phase transitions
takes advantage of the fact that the partition function can be fully characterized by its zeros in the complex plane of q {\displaystyle q} . These zeros
Lee–Yang_theory
Combinatorial optimization method
cutting planes that are violated by x {\displaystyle x} . If any are found, add them to the LP relaxation and return to 3.2. Branch to partition the problem
Branch_and_cut
Decomposition into connected open cells of lower dimensions, by a finite set of objects
vector spaces have also been studied; since complex lines do not partition the complex plane into multiple connected components, the combinatorics of vertices
Arrangement_(space_partition)
Bisection of Euclidean space by a hyperplane
into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a half-plane (open or closed)
Half-space_(geometry)
Video game templates
(or plane) in 3D space, where a, b, and c are coefficients that determine the orientation of the plane, and d is a constant that shifts the plane along
Brush_(video_games)
sodateyou!" (Japanese: 花火を育てよう！) August 16, 2013 (2013-08-16) 570 "The Partitioning Hammer" Transliteration: "Bunshin hanmā" (Japanese: 分身ハンマー) August 16
List of Doraemon (2005 TV series) episodes (2005–2014)
List_of_Doraemon_(2005_TV_series)_episodes_(2005–2014)
Country in Northwestern Europe
formed the United Kingdom of Great Britain and Ireland. Following the partition of Ireland and the independence of the Irish Free State in 1922, which
United_Kingdom
Office furniture meant to allow for concentration
an enclosed office that is separated from neighboring workspaces, with partitions that are usually 5–6 feet (1.5–1.8 m) tall. Its purpose is to isolate
Cubicle
Visual representation of a mathematical relationship
vector on a diagram called an Argand diagram. The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named
Mathematical_diagram
Country in South Asia
Indian Empire was partitioned into the independent dominions of a Hindu-majority India and a Muslim-majority Pakistan. The partition brought large-scale
India
Operation in calculus
thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the
Integral
British mandate territory (1920–1948)
1944–1948 Jewish insurgency in Mandatory Palestine. The United Nations Partition Plan for Palestine, adopted by the UN General Assembly in November 1947
Mandatory_Palestine
Property of a mathematical space
sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D)
Dimension
Area in Warsaw, Poland
191 people. At the turn of the 20th century, the land of Mokotów was partitioned and sold for housing development, and numerous new streets were created
Upper_Mokotów
Country in Central Europe
With the passing of the prosperous Polish Golden Age, the country was partitioned by neighbouring states at the end of the 18th century. At the end of
Poland
Well studied projective geometries over finite fields
incompatibility (help) Yff, Peter (1977). "On subplane partitions of a finite projective plane". Journal of Combinatorial Theory, Series A. 22 (1): 118–122
Spread_(projective_geometry)
Founder and 1st Governor-General of Pakistan (1876–1948)
the idea of partition. Nehru stated in 1960, "the truth is that we were tired men and we were getting on in years ... The plan for partition offered a way
Muhammad_Ali_Jinnah
First Lady of Pakistan (1931–1996)
as the First Lady of Pakistan from 1977 until her husband's death in a plane crash in 1988. As First Lady, her work highlighted the lives of disabled
Shafiq_Zia
Indian drama television series
learns Mihir never returned, reclaims Shanti Niketan, and removes the partition in the house. She supports Vaishnavi against Karan and Gautam, and Nakul
Kyunki Saas Bhi Kabhi Bahu Thi 2
Kyunki_Saas_Bhi_Kabhi_Bahu_Thi_2
Algorithm used for points in euclidean space
geometry is partitioned into elements with simpler shapes; for instance, two-dimensional domains (either subsets of the Euclidean plane or surfaces in
Lloyd's_algorithm
ISBN 0-9521163-0-8 John Strawson, author of Encountering Islamic law, Partitioning Palestine: Legal Fundamentalism in the Palestinian-Israeli Conflict and
List of British Jewish writers
List_of_British_Jewish_writers
Special type of projective plane
translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation
Translation_plane
Technique of illustration
reference system of two viewing planes: horizontal H ("ground") and vertical V ("backdrop"). These two planes intersect to partition 3D space into four quadrants
Multiview orthographic projection
Multiview_orthographic_projection
Since the partition of British India in 1947 and subsequent creation of the dominions of India and Pakistan, the two countries have been involved in a
India–Pakistan wars and conflicts
India–Pakistan_wars_and_conflicts
Integral transform useful in probability theory, physics, and engineering
s} (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions are often denoted using a lowercase symbol for the time-domain
Laplace_transform
Concept that permeates much of inferential statistics and descriptive statistics
The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning
Partition_of_sums_of_squares
Country in South Asia
All-India Muslim League, Pakistan gained independence in 1947 after the partition of British India, which awarded separate statehood to its Muslim-majority
Pakistan
European wide-body airliner
expressed public interest in purchasing such a plane, Airbus was already pursuing its own large-plane project. Analysts suggested that Boeing would instead
Airbus_A380
Country in Southeastern Europe and West Asia
Armistice of Mudros in 1918, the victorious Allied Powers sought the partition of the Ottoman Empire through the 1920 Treaty of Sèvres. The occupation
Turkey
cross-pollination": the "loft-like" laboratories are equipped with modular partitions and demountable casework (cabinetry, bookshelves, and the like), the firm's
List of works by Rafael Viñoly
List_of_works_by_Rafael_Viñoly
Polyhedron with eight triangular faces
of it: Triangular antiprisms: Two faces are equilateral, lie on parallel planes, and have a common axis of symmetry. The other six triangles are isosceles
Octahedron
Sea Fleet under joint command (and Soviet Navy flag) until a full-scale partition agreement could be reached. Formally, the Fleet's Commander was to be
History_of_the_Russian_Navy
Skilled trade
..acoustical ceilings, computer-access flooring, metal framing, wall partitions, office furniture systems, and both custom or factory-produced materials
Carpentry
travel, tourism, insurance
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
PLANE PARTITION
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