G. W. Peck is a pseudonymous attribution used as the author or co-author of a number of published mathematics academic papers. Peck is sometimes humorously identified with George Wilbur Peck, a former governor of the US state of Wisconsin. [1]
Peck first appeared as the official author of a 1979 paper entitled "Maximum antichains of rectangular arrays". [2] The name "G. W. Peck" is derived from the initials of the actual writers of this paper: Ronald Graham, Douglas West, George B. Purdy, Paul Erdős, Fan Chung, and Daniel Kleitman. The paper initially listed Peck's affiliation as Xanadu, but the editor of the journal objected, so Ron Graham gave him a job at Bell Labs. Since then, Peck's name has appeared on some sixteen publications, [3] primarily as a pseudonym of Daniel Kleitman. [1]
In reference to "G. W. Peck", Richard P. Stanley defined a Peck poset to be a graded partially ordered set that is rank symmetric, rank unimodal, and strongly Sperner. [4] The posets in the original paper by G. W. Peck are not quite Peck posets, as they lack the property of being rank symmetric.
The Erdős number describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
Ronald Lewis Graham was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences.
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.
In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician Robert P. Dilworth (1950).
In mathematics, in the branch of combinatorics, a graded poset is a partially ordered set (poset) P equipped with a rank functionρ from P to the set N of all natural numbers. ρ must satisfy the following two properties:
A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the person is separated from American actor Kevin Bacon. The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment.
Daniel J. Kleitman is an American mathematician and professor of applied mathematics at MIT. His research interests include combinatorics, graph theory, genomics, and operations research.
In mathematics, a representation is a very general relationship that expresses similarities between mathematical objects or structures. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects yi conform, in some consistent way, to those existing among the corresponding represented objects xi. More specifically, given a set Π of properties and relations, a Π-representation of some structure X is a structure Y that is the image of X under a homomorphism that preserves Π. The label representation is sometimes also applied to the homomorphism itself.
In mathematics, a power of three is a number of the form 3n where n is an integer – that is, the result of exponentiation with number three as the base and integer n as the exponent.
In mathematics, Young's lattice is a lattice that is formed by all integer partitions. It is named after Alfred Young, who, in a series of papers On quantitative substitutional analysis, developed the representation theory of the symmetric group. In Young's theory, the objects now called Young diagrams and the partial order on them played a key, even decisive, role. Young's lattice prominently figures in algebraic combinatorics, forming the simplest example of a differential poset in the sense of Stanley (1988). It is also closely connected with the crystal bases for affine Lie algebras.
In mathematics, a fence, also called a zigzag poset, is a partially ordered set in which the order relations form a path with alternating orientations:
Douglas Brent West is a professor of graph theory at University of Illinois at Urbana-Champaign. He received his Ph.D. from Massachusetts Institute of Technology in 1978; his advisor was Daniel Kleitman. He is the "W" in G. W. Peck, a pseudonym for a group of six mathematicians that includes West. He is the editor of the journal Discrete Mathematics.
In the mathematical theory of infinite graphs, the Erdős–Dushnik–Miller theorem is a form of Ramsey's theorem stating that every infinite graph contains either a countably infinite independent set, or a clique with the same cardinality as the whole graph.
George Barry Purdy was a mathematician and computer scientist who specialized in cryptography, combinatorial geometry and number theory. Purdy received his Ph.D. from the University of Illinois at Urbana–Champaign in 1972, officially under the supervision of Paul T. Bateman, but his de facto adviser was Paul Erdős. He was on the faculty in the mathematics department at Texas A&M University for 11 years, and was appointed the Geier Professor of computer science at the University of Cincinnati in 1986.
In order-theoretic mathematics, a graded partially ordered set is said to have the Sperner property, if no antichain within it is larger than the largest rank level in the poset. Since every rank level is itself an antichain, the Sperner property is equivalently the property that some rank level is a maximum antichain. The Sperner property and Sperner posets are named after Emanuel Sperner, who proved Sperner's theorem stating that the family of all subsets of a finite set has this property. The lattice of partitions of a finite set typically lacks the Sperner property.
In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of a partition of the order into a minimum number of antichains. It is named for Leon Mirsky (1971) and is closely related to Dilworth's theorem on the widths of partial orders, to the perfection of comparability graphs, to the Gallai–Hasse–Roy–Vitaver theorem relating longest paths and colorings in graphs, and to the Erdős–Szekeres theorem on monotonic subsequences.
Jon Hal Folkman was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
In mathematics, a differential poset is a partially ordered set satisfying certain local properties. This family of posets was introduced by Stanley (1988) as a generalization of Young's lattice, many of whose combinatorial properties are shared by all differential posets. In addition to Young's lattice, the other most significant example of a differential poset is the Young–Fibonacci lattice.
Curtis Greene is an American mathematician, specializing in algebraic combinatorics. He is the J. McLain King Professor of Mathematics at Haverford College in Pennsylvania.
In mathematics, an incidence poset or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges of an undirected graph. The incidence poset of a graph G has an element for each vertex or edge in G; in this poset, there is an order relation x ≤ y if and only if either x = y or x is a vertex, y is an edge, and x is an endpoint of y.