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Graph of numbers differing by a square
Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic
Paley_graph
Concept in graph theory
srg(275, 112, 30, 56). The Paley graph of order q is an srg(q, (q − 1)/2, (q − 5)/4, (q − 1)/4). The smallest Paley graph, with q = 5, is the 5-cycle
Strongly_regular_graph
English mathematician
sizes of matrices for which Hadamard matrices exist. The Paley graphs and Paley tournaments in graph theory are closely related, although they do not appear
Raymond_Paley
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
numbers, any Paley graph is a circulant graph. Every Möbius ladder is a circulant graph, as is every complete graph. A complete bipartite graph is a circulant
Circulant_graph
Cycle graph plus universal vertex
subgraph, while neither the 17-vertex Paley graph nor its complement contains a copy of K4. Weisstein, Eric W. "Wheel Graph". MathWorld. Rosen, Kenneth H. (2011)
Wheel_graph
Graph which is isomorphic to its complement
4-vertex path graph and the 5-vertex cycle graph. Every Paley graph is self-complementary. For example, the 3 × 3 rook's graph (the Paley graph of order nine)
Self-complementary_graph
Mapping a graph onto itself without changing edge-vertex connectivity
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving
Graph_automorphism
Infinite graph containing all countable graphs
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with
Rado_graph
Spectral graph theory concept
-2} , so it is a 3-regular Ramanujan graph. The icosahedral graph is a 5-regular Ramanujan graph. A Paley graph of order q {\displaystyle q} is q − 1
Ramanujan_graph
Special case of a strongly regular graph
existence of a conference graph is unknown. The smallest value of v which has no Paley graph but does have a conference graph is v = 45, found in 1978
Conference_graph
Graph where every edge is in one triangle
instance, the nine-vertex Paley graph (the graph of the 3-3 duoprism) is the Cartesian product of two triangles. The Hamming graph H ( d , 3 ) {\displaystyle
Locally_linear_graph
On existence of a strongly regular graph
These two graphs are the nine-vertex Paley graph (the graph of the 3-3 duoprism) with parameters (9,4,1,2) and the Berlekamp–van Lint–Seidel graph with parameters
Conway's_99-graph_problem
graph Cameron graph Petersen graph Hall–Janko graph Hoffman–Singleton graph Higman–Sims graph Paley graph of order 13 Shrikhande graph Schläfli graph
List_of_graphs
Subgraph induced by all nodes linked to a given node of a graph
locally C4 graph, the icosahedron is the unique connected locally C5 graph, and the Paley graph of order 13 is locally C6. Locally cyclic graphs other than
Neighbourhood_(graph_theory)
Mathematical group that can be generated as the set of powers of a single element
graph is a cycle graph, and for an infinite cyclic group with its generator the Cayley graph is a doubly infinite path graph. However, Cayley graphs can
Cyclic_group
parameters differing by one, it is the only graph that is not a Paley graph. It is also an integral graph, meaning that the eigenvalues of its adjacency
Berlekamp–Van Lint–Seidel graph
Berlekamp–Van_Lint–Seidel_graph
≡ 0 mod 4 {\displaystyle m\,\equiv \,0\mod 4} for m < 668. Paley biplane Paley graph Paley, R.E.A.C. (1933). "On orthogonal matrices". Journal of Mathematics
Paley_construction
Statement in mathematical combinatorics
among 6.4 × 1022 different 2-colourings of 16-node graphs, and only one (4, 4, 17) graph (the Paley graph of order 17) among 2.46 × 1026 colourings. It follows
Ramsey's_theorem
regular graph. The Brouwer–Haemers graph has several related algebraic constructions. One of the simplest is as a degree-4 generalized Paley graph: it can
Brouwer–Haemers_graph
Prime number congruent to 1 mod 4
exists a Paley graph with p {\displaystyle p} vertices, representing the numbers modulo p {\displaystyle p} , with two numbers adjacent in the graph if and
Pythagorean_prime
Linear algebra matrix
full-length cycle. The Möbius ladders are examples of circulant graphs, as are the Paley graphs for fields of prime order. Davis, Philip J (1970). Circulant
Circulant_matrix
F11; the first is equivalent to an exceptional action on 11 points, related to the Paley biplane. distanceregular.org page on Livingstone Graph v t e
Livingstone_graph
the graph is planar and F indicates that the graph is not planar. Wikimedia Commons has media related to Graphs by number of vertices. See also Graph theory
List of graphs by edges and vertices
List_of_graphs_by_edges_and_vertices
toroidal graph, a locally linear graph, a strongly regular graph with parameters (9,4,1,2), the 3 × 3 {\displaystyle 3\times 3} rook's graph, and the Paley graph
3-3_duoprism
Mathematical problem
multiple of 4. Additional examples were later constructed by Scarpis and Paley and subsequently by many other authors. Such matrices are now known as Hadamard
Hadamard's maximal determinant problem
Hadamard's_maximal_determinant_problem
mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or (6,3)-problem asks for the maximum number of edges in a graph in which every edge belongs
Ruzsa–Szemerédi_problem
Matrix in math with special properties
then the Paley graphs provide examples of symmetric conference matrices of order n, by taking S to be the Seidel matrix of the Paley graph. The first
Conference_matrix
Integer that is a perfect square modulo some integer
quadratic residues. Paley graphs are dense undirected graphs, one for each prime p ≡ 1 (mod 4), that form an infinite family of conference graphs, which yield
Quadratic_residue
Algebraic structure
application in combinatorics, two well known examples being the definition of Paley Graphs and the related construction for Hadamard Matrices. In arithmetic combinatorics
Finite_field
hexagonal faces. The dual graph for this embedding is isomorphic to the Paley graph of order 13. The chromatic number of the F26A graph is 2. The chromatic
F26A_graph
only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of
Horrocks–Mumford_bundle
Directed graph where each vertex pair has one arc
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently
Tournament_(graph_theory)
Month of 1933
Raymond Paley, 26, English mathematician who discovered the Paley construction for Hadamard matrices, the Paley graphs in graph theory, the Paley–Wiener
April_1933
Linear operator on dense subset of its apparent domain
extension is the Paley–Wiener map. Blumberg theorem – Any real function on R admits a continuous restriction on a dense subset of R Closed graph theorem (functional
Densely_defined_operator
Structure in combinatorial mathematics
5; a 2-(11,5,2)), and is also known as the Paley biplane after Raymond Paley; it is associated to the Paley digraph of order 11, which is constructed using
Block_design
Method in probability theory
estimate of the previous theorem can be refined by means of the so-called Paley–Zygmund inequality. Suppose that Xn is a sequence of non-negative real-valued
Second_moment_method
Mathematical inequality relating inner products and norms
sums of squares Minkowski inequality – Triangle inequality in Lp spaces Paley–Zygmund inequality – Probability equation in mathematics O'Connor, J.J.;
Cauchy–Schwarz_inequality
Mathematical classification
of small integers – 1 through 6, depending on the graph. The ordinary ADE graphs are the only graphs that admit a positive labeling with the following
ADE_classification
Mathematical inequality explaining concentration of random variables
}}\end{cases}}} In contrast to most commonly used concentration inequalities, the Paley-Zygmund inequality provides a lower bound on the deviation probability.
Concentration_inequality
theorem (graph theory) Nicomachus's theorem (number theory) Ore's theorem (graph theory) Paley's theorem (algebra) Perfect graph theorem (graph theory)
List_of_theorems
1980 book and film by William H. Whyte
forecourts or public spaces associated with modern commercial office towers. Paley Park and Greenacre Park were included as they are predominantly paved public
The Social Life of Small Urban Spaces
The_Social_Life_of_Small_Urban_Spaces
American business executive (born 1973)
on the board of directors of Starbucks and the board of trustees for the Paley Center for Media. He also serves on the Advisory Council of the Stanford
Neal_Mohan
British economist (1842–1924)
Cambridge, and became lecturer in the moral sciences in 1868. He taught Mary Paley who became a lecturer at the then embryonic Newnham College, Cambridge;
Alfred_Marshall
Bound on probability of a random variable being far from its mean
log-concave densities. Several other related inequalities are also known. The Paley–Zygmund inequality gives a lower bound on tail probabilities, as opposed
Chebyshev's_inequality
Area of mathematical analysis
singular integrals, oscillatory integrals, Fourier multipliers, Littlewood–Paley theory, and spectral decompositions. A related tradition is abstract harmonic
Harmonic_analysis
Integral transform useful in probability theory, physics, and engineering
predecessors of the modern table of Laplace transforms. In 1934, Raymond Paley and Norbert Wiener published the important work Fourier transforms in the
Laplace_transform
Prussian military theorist (1780–1831)
argued that war could not be quantified or reduced to mapwork, geometry, and graphs. Clausewitz had many aphorisms, of which one of the most famous is, "War
Carl_von_Clausewitz
inequality / (1:R) McDiarmid's inequality Multidimensional Chebyshev's inequality Paley–Zygmund inequality / (1:R) Pinsker's inequality / (2:R) Vysochanskiï–Petunin
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Supposition or system of ideas intended to explain something
K-theory — KK-theory — Knot theory — L-theory — Lie theory — Littlewood–Paley theory — Matrix theory — Measure theory — Model theory — Module theory —
Theory
and Mervin Edgar Muller. Independently pre-discovered by Raymond E. A. C. Paley and Norbert Wiener in 1934. 1956 – Kruskal's algorithm developed by Joseph
Timeline_of_algorithms
American sitcom (2005–2014)
9, 2014. "Alyson Hannigan – "How I Met Your Mother" Sitcom – William S. Paley TV Fest". Whedon.info. March 28, 2006. Archived from the original on November
How_I_Met_Your_Mother
U.S.-led campaign against illegal drug use and trade
10, 2026. Paley, Dawn (2014). Drug War Capitalism. Edinburgh: AK Press. Paley, Dawn (2014). Drug War Capitalism. Edinburgh: AK Press. Paley, Dawn (2014)
War_on_drugs
Mathematics concept
subsequently constructed by Hadamard (in 1893). In 1933, Raymond Paley discovered the Paley construction, which produces a Hadamard matrix of order q + 1
Hadamard_matrix
Former federal electoral district in Alberta, Canada
Graph of election results in Edmonton Mill Woods (minor parties that never got 2% of the vote or didn't run consistently are omitted)
Edmonton Mill Woods (federal electoral district)
Edmonton_Mill_Woods_(federal_electoral_district)
YANKEES} (TV)". The Paley Center for Media. "WORLD SERIES, 1952: GAME 6 {BROOKLYN DODGERS VS. NEW YORK YANKEES} (TV)". The Paley Center for Media. Larry
History of Major League Baseball on NBC
History_of_Major_League_Baseball_on_NBC
Integral transform and linear operator
the result aggregates much work of others, including Hardy, Paley and Wiener (see Paley–Wiener theorem), as well as work by Riesz, Hille, and Tamarkin
Hilbert_transform
Change in the heritable traits of populations
meantime, Ray's ideas of benevolent design had been developed by William Paley into the Natural Theology or Evidences of the Existence and Attributes of
Evolution
Social science studying goods and services
popularised by such neoclassical economists as Alfred Marshall and Mary Paley Marshall as a concise synonym for "economic science" and a substitute for
Economics
American fantasy drama television series
Graph of the US viewing figures of the first three seasons of True Blood.
True_Blood
Concept in economics and decision theory
Individuals' consumptions are constrained by their budget allowance. The graph of budget line is a linear, downward-sloping line between X and Y axes.
Utility
Irish mathematician and physicist (1805–1865)
Science". Studies in Romanticism. 51 (4): 490. ISSN 0039-3762. JSTOR 24247229. Paley, Morton D. (1999). Coleridge's Later Poetry. Clarendon Press. p. 26.
William_Rowan_Hamilton
Construction in group theory
determine two lines (respectively, points). In this case (the Paley biplane, obtained from the Paley digraph of order 11), the points are the affine line (the
Projective_linear_group
American author
assistant at Avalon Books and the Museum of Television and Radio (now the Paley Center for Media). She became a freelance copyeditor for magazines to focus
Lynn_Messina
Algorithm in utilitarian ethics
his science of utility applied to economics. He described utility with graphs where marginal utility continuously declines. His figure 9 on page 173 has
Felicific_calculus
Exponentially decreasing bounds on tail distributions of random variables
bound from below on the tail probabilities can be obtained by applying the Paley-Zygmund inequality to e t X {\displaystyle e^{tX}} , yielding: P ( X >
Chernoff_bound
creativecommons.org "Ahimsa: Sita Sings the Blues now CC-0 "Public Domain" « Nina Paley's Blog". blog.ninapaley.com. 18 January 2013. Retrieved 7 July 2018. amy
List of major Creative Commons–licensed works
List_of_major_Creative_Commons–licensed_works
Analysis of variance Analytic and enumerative statistical studies Ancestral graph Anchor test Ancillary statistic ANCOVA – redirects to Analysis of covariance
List_of_statistics_articles
Stringy Woodcutter and Ned in Wolfwalkers), dies at age 66. November 20: Andy Paley, American songwriter, composer, and record producer (Nickelodeon Animation
2024_in_animation
Evolutionary process
as the work of a deity and as evidence for the existence of God. William Paley believed that organisms were perfectly adapted to the lives they led, an
Adaptation
Smooth and compactly supported function
since the only entire analytic bump function is the zero function (see Paley–Wiener theorem and Liouville's theorem). Because the bump function is infinitely
Bump_function
Type of complex function with growth bounded by an exponential function
}\exp \left[-\left(\tau +{\frac {1}{n}}\right)|z|\right]|f(z)|.} Paley–Wiener theorem Paley–Wiener space In fact, even ( max | z | = r log log | F ( z
Exponential_type
Treatise by Thomas Malthus
The 1st edition influenced writers of natural theology such as William Paley and Thomas Chalmers. Following both widespread praise and criticism of his
An Essay on the Principle of Population
An_Essay_on_the_Principle_of_Population
Form of biological modelling
D402–D406. doi:10.1093/nar/gkz1054. PMC 7145653. PMID 31696234. Karp PD, Paley SM, Krummenacker M, Latendresse M, Dale JM, Lee TJ, et al. (January 2010)
Metabolic_network_modelling
Linear programming algorithm
Klemens" (PDF). Journal of Intellectual Property Law. 16: 214–223. Mark A. Paley (1995). "The Karmarkar Patent: Why Congress Should "Open the Door" to Algorithms
Karmarkar's_algorithm
French visual artist (1926–2005)
Christine Macel, Tom MacDonough, Christian Schlatter and Aude Bodet, Goldie Paley Gallery/Moore college of art and design (Ed.):Philadelphie, 2002 [catalogue]
Raymond_Hains
Museum in Manhattan, New York
Modern Art New York Public Library Main Branch New York Transit Museum Paley Center for Media Scandinavia House United Nations Art Collection Upper West
National Museum of Mathematics
National_Museum_of_Mathematics
space and E− is a monogenic function in lower half space. There is also a Paley–Wiener theorem in n-Euclidean space arising in Clifford analysis. Many Dirac
Clifford_analysis
physician and psychologist, and pioneer in cheminformatics and chemical graph theory Annette Aiello (B.A. 1972), entomologist at the Smithsonian Tropical
List of Brooklyn College alumni
List_of_Brooklyn_College_alumni
World Series: Los Angeles Dodgers vs. New York Yankees {GAME 6} (TV)". The Paley Center for Media. Shales, Tom (October 13, 1977). "Howard Cosell". The Washington
History of Major League Baseball on ABC
History_of_Major_League_Baseball_on_ABC
Annual session of lectures
University): Differential equations from the algebraic standpoint. 1934 Raymond Paley (Trinity College, Cambridge University), deceased in 1933 and replaced by
Colloquium_Lectures_(AMS)
Overview of the events of 2022 in science
Bryn; Newton, Taylor; Ravier, Jimmy; Kinany, Nawal; D'Ercole, Marina; Paley, Aurélie; Hankov, Nicolas; Varescon, Camille; McCracken, Laura; Vat, Molywan;
January–March_2022_in_science
American short-lived television broadcasting joint venture
All-Star Game} 1995 (TV)". The Paley Center for Media. "All-Star Selection Special {Baseball}, the 1995 (TV)". The Paley Center for Media. Kent, Milton
The_Baseball_Network
American artist (1907–2007)
the loom moved and this experience inspired a series of ink drawings on graph paper. This eight-piece series would later inspire the 1990s series, Drawings
Lenore_Tawney
Tropiano 2002, p. 280. "Hill Street Blues: Queen For A Day (TV)". The Paley Center for Media. "Hill Street Blues - Season 5 Episode 21, Queen for a
List of dramatic television series with LGBTQ characters: 1960s–2000s
List_of_dramatic_television_series_with_LGBTQ_characters:_1960s–2000s
Village and civil parish in North Yorkshire, England
and then extensively restored in the late 1870s by Lancaster architects Paley and Austin. The church features a war memorial to those from the village
Thorpe_Bassett
French films released in 1934
French Cinema. p.41 Bock, Hans-Michael & Bergfelder, Tim. The Concise CineGraph. Encyclopedia of German Cinema. p.462 Hayward, Susan. French National Cinema
List_of_French_films_of_1934
PALEY GRAPH
PALEY GRAPH
Surname or Lastname
English
English : variant of Parsley.Scottish : variant of Paisley. Black suggests also that some examples of Pasley and Paisley may be derived from a place known as Pasley or Howpasley, in the Borders region.Possibly an altered spelling of German Pasler, a variant of Basler, or of Pässler, an occupational name, from an agent derivative of basteln ‘to do handicraft’.
Surname or Lastname
English
English : variant spelling of Ely.
Surname or Lastname
English
English : habitational name from Padley in Derbyshire or Padley Common in Devon. The place in Derbyshire was named probably with the Old English personal name Padda + lēah ‘glade’, ‘woodland clearing’. Alternatively, the first element may have been padde ‘toad’.
Surname or Lastname
English
English : habitational name from any of several minor places in Lincolnshire and Shropshire (Apley) or the Isle of Wight and Somerset (Appley), named with Old English æppel ‘apple’ + lēah ‘woodland clearing’.
Surname or Lastname
English
English : probably a variant of Fawley.
Surname or Lastname
English
English : variant spelling of Galley.Ukrainian : nickname meaning ‘hasten’, ‘hurry’, from Proto-Slavic galiti ‘to shout’.
Female
English
Variant spelling of English Kayley, KALEY means "slender."
Surname or Lastname
Americanized spelling of German Kahle. Compare Kahley or Köhler (see Kohler).English and Manx
Americanized spelling of German Kahle. Compare Kahley or Köhler (see Kohler).English and Manx : variant spelling of Caley.
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from Pavilly in Seine-Maritime, which is named with the Gallo-Roman personal name Pavilius + the locative suffix -acum.English : from a pet form of Paul.Possibly an altered spelling of Pauli.
Surname or Lastname
English
English : from a medieval pet form of Paul.German : variant or derivative of Paul. Compare Poley.
Male
English
Pet form of English Pace, PACEY means "Passover; Easter."
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from places in Eure and Seine-Maritime, France, called Cailly, from a Romano-Gallic personal name Callius + the locative suffix -acum.English : habitational name from a minor place called Caley in the parish of Winwick, Lancashire, named with Old English cÄ â€˜jackdaw’ + lÄ“ah ‘woodland clearing’.Irish : reduced and altered form of McCauley.Manx : variant of Callow.
Surname or Lastname
English
English : from a pet form of Pate 1.
Female
English
Variant spelling of English Hayley, HALEY means "hay field."
Surname or Lastname
English (chiefly West Yorkshire)
English (chiefly West Yorkshire) : habitational name from any of several places named with Old English hēg ‘hay’ + lēah ‘wood’, ‘clearing’.
Surname or Lastname
English (southern)
English (southern) : from the medieval female personal name Pavia, which is of uncertain origin. Reaney and Wilson suggest it may be from Old French pavie ‘peach’ or Pavie ‘woman from Pavia’ (see 2).English (southern) : habitational name from Pavia in Lombardy, Italy.English (southern) : variant of Paver.
Surname or Lastname
English
English : unexplained.
Girl/Female
Indian
Hay field
Surname or Lastname
English
English : variant of Raleigh.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : possibly a nickname for someone with pale or lustreless eyes, from Middle English pale ‘pale’ + eye ‘eye’.English : from an Old Scandinavian personal name, Old Danish Palli or Old Swedish Palle, probably originally an ethnic name meaning ‘Pole’.French : habitational name from a place in Seine-et-Marne, probably originally derived from Latin palus ‘post’, ‘stake’ + suffix -etum.Jewish (from Belarus), Belorussian, and Ukrainian : occupational name for a distiller, from an eastern Slavic word meaning ‘to burn’ (Russian palit, Ukrainian palyty) + the Slavic noun suffix -ej.
PALEY GRAPH
PALEY GRAPH
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : unexplained.
Girl/Female
Indian
Charitable and kind
Girl/Female
Australian, Dutch, Hebrew
Gift from God
Girl/Female
Indian, Kannada, Traditional
Goddess Parvati
Female
Scandinavian
Variant spelling of Scandinavian Dagny, DAGNEY means "new day."
Girl/Female
Hindu, Indian, Traditional
Goddess Lakshmi; Describer of the Gods
Boy/Male
Hindu, Indian, Punjabi, Sikh
Resident of the Beauteous Realm
Boy/Male
Muslim
Lion
Girl/Female
Indian, Telugu
Tradition
Surname or Lastname
English
English : from Middle English diche, dike, Old English dīc ‘dike’, ‘earthwork’, hence a metonymic occupational name for a ditcher or a topographic name for someone who lived by a ditch or dike. The medieval dike was larger and more prominent than the modern ditch, and was usually constructed for purposes of defense rather than drainage.Americanized spelling of Dutch Dijk (see Dyck).
PALEY GRAPH
PALEY GRAPH
PALEY GRAPH
PALEY GRAPH
PALEY GRAPH
p. pr. & vb. n.
of Palsy
v. i.
Wanting in color; not ruddy; dusky white; pallid; wan; as, a pale face; a pale red; a pale blue.
p. pr. & vb. n.
of Parley
v. t.
To inclose with pales, or as with pales; to encircle; to encompass; to fence off.
v. t.
To make pale; to diminish the brightness of.
n.
Same as Palea.
v. i.
To turn pale; to lose color or luster.
v. i.
Not bright or brilliant; of a faint luster or hue; dim; as, the pale light of the moon.
a.
Divided by pallets, or pales; paly.
n.
Palsy.
a.
Paly, and then divided fesswise, so that each vertical piece is cut into two, having the colors used alternately or counterchanged. Thus the escutcheon in the illustration may also be blazoned paly of six per fess counterchanged argent and azure.
imp. & p. p.
of Pale
n.
The pale, purplish color of lavender flowers, paler and more delicate than lilac.
imp. & p. p.
of Parley
a.
In a pale manner; dimly; wanly; not freshly or ruddily.
a.
Pale; wanting color; dim.
n.
A perpendicular band upon an escutcheon, one half the breadth of the pale.
a.
Bearing palms; abounding in palms; derived from palms; as, a palmy shore.
pl.
of Parley
v. t.
To affect with palsy, or as with palsy; to deprive of action or energy; to paralyze.