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Tripod Packing
In combinatorics, tripod packing is a problem of finding many disjoint tripods in a three-dimensional grid, where a tripod is an infinite polycube, the union of the grid cubes along three positive axis-aligned rays with a shared apex. Several problems of tiling and packing tripods and related shapes were formulated in 1967 by Sherman K. Stein. Stein originally called the tripods of this problem "semicrosses", and they were also called Stein corners by Solomon W. Golomb. A collection of disjoint tripods can be represented compactly as a monotonic matrix, a square matrix whose nonzero entries increase along each row and column and whose equal nonzero entries are placed in a monotonic sequence of cells, and the problem can also be formulated in terms of finding sets of triples satisfying a compatibility condition called "2-comparability", or of finding compatible sets of triangles in a convex polygon. The best lower bound known for the number of tripods that can have their apexes p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tripod Packing
In combinatorics, tripod packing is a problem of finding many disjoint tripods in a three-dimensional grid, where a tripod is an infinite polycube, the union of the grid cubes along three positive axis-aligned rays with a shared apex. Several problems of tiling and packing tripods and related shapes were formulated in 1967 by Sherman K. Stein. Stein originally called the tripods of this problem "semicrosses", and they were also called Stein corners by Solomon W. Golomb. A collection of disjoint tripods can be represented compactly as a monotonic matrix, a square matrix whose nonzero entries increase along each row and column and whose equal nonzero entries are placed in a monotonic sequence of cells, and the problem can also be formulated in terms of finding sets of triples satisfying a compatibility condition called "2-comparability", or of finding compatible sets of triangles in a convex polygon. The best lower bound known for the number of tripods that can have their apexes p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polycube
upAll 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total A puzzle involving arranging nine L tricubes into a 3×3 cube A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes. Enumerating polycubes A chiral pentacube Like polyominoes, polycubes can be enumerated in two ways, depending on whether chiral pairs of polycubes are counted as one polycube or two. For example, 6 tetracubes have mirror symmetry and one is chiral, giving a count of 7 or 8 tetracubes respectively. Unlike polyominoes, polycubes are usually counted with mirror pairs distinguished, because one cannot turn a polycube over to reflect it as one can a polyomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sherman K
Sherman most commonly refers to: *Sherman (name), a surname and given name (and list of persons with the name) ** William Tecumseh Sherman (1820–1891), American Civil War General *M4 Sherman, a tank Sherman may also refer to: Places United States * Sherman Island (California) * Mount Sherman, Colorado * Sherman, Connecticut, a New England town ** Sherman (CDP), Connecticut, the central village in the town * Sherman, Illinois, a village * Sherman, Kansas * Sherman, Kentucky * Sherman, Maine, a town * Sherman, Michigan, an unincorporated community * Sherman, Minnesota, an unincorporated community * Sherman, Mississippi, a town * Sherman, Missouri, an unincorporated community * Sherman, New Mexico, an unincorporated community * Sherman (town), New York ** Sherman (village), New York * Sherman, South Dakota, a town * Sherman, Texas, a city * Sherman, Washington, a ghost town * Sherman, West Virginia, an unincorporated community * Sherman, Clark County, Wisconsin, a town ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solomon W
Solomon (; , ),, ; ar, سُلَيْمَان, ', , ; el, Σολομών, ; la, Salomon also called Jedidiah ( Hebrew: , Modern: , Tiberian: ''Yăḏīḏăyāh'', "beloved of Yah"), was a monarch of ancient Israel and the son and successor of David, according to the Hebrew Bible and the Old Testament. He is described as having been the penultimate ruler of an amalgamated Israel and Judah. The hypothesized dates of Solomon's reign are 970–931 BCE. After his death, his son and successor Rehoboam would adopt harsh policy towards the northern tribes, eventually leading to the splitting of the Israelites between the Kingdom of Israel in the north and the Kingdom of Judah in the south. Following the split, his patrilineal descendants ruled over Judah alone. The Bible says Solomon built the First Temple in Jerusalem, dedicating the temple to Yahweh, or God in Judaism. Solomon is portrayed as wealthy, wise and powerful, and as one of the 48 Jewish prophets. He is also the su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big Omega Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for ''Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rates: di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locally Linear Graph
In graph theory, a locally linear graph is an undirected graph in which every edge belongs to exactly one triangle. Equivalently, for each vertex of the graph, its neighbors are each adjacent to exactly one other neighbor, so the neighbors can be paired up into an induced matching. Locally linear graphs have also been called locally matched graphs. Many constructions for locally linear graphs are known. Examples of locally linear graphs include the triangular cactus graphs, the line graphs of 3-regular triangle-free graphs, and the Cartesian products of smaller locally linear graphs. Certain Kneser graphs, and certain strongly regular graphs, are also locally linear. The question of how many edges locally linear graphs can have is one of the formulations of the Ruzsa–Szemerédi problem. Although dense graphs can have a number of edges proportional to the square of the number of vertices, locally linear graphs have a smaller number of edges, falling short of the square by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruzsa–Szemerédi Problem
In combinatorial 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 to a unique triangle. Equivalently it asks for the maximum number of edges in a balanced bipartite graph whose edges can be partitioned into a linear number of induced matchings, or the maximum number of triples one can choose from n points so that every six points contain at most two triples. The problem is named after Imre Z. Ruzsa and Endre Szemerédi, who first proved that its answer is smaller than n^2 by a slowly-growing (but still unknown) factor. Equivalence between formulations The following questions all have answers that are asymptotically equivalent: they differ by, at most, constant factors from each other. *What is the maximum possible number of edges in a graph with n vertices in which every edge belongs to a unique triangle? The graphs with this property are called locally linear graphs o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Journal Of Combinatorics
The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin (Georgia Institute of Technology). The Electronic Journal of Combinatorics is a founding member of the Free Journal Network. According to the ''Journal Citation Reports'', the journal had a 2017 impact factor of 0.762. Editors-in-chief Current The current editors-in-chief are: * Maria Axenovich, Karlsruhe Institute of Technology, Germany * Miklós Bóna, University of Florida, United States * Julia Böttcher, London School of Economics, United Kingdom * Richard A. Brualdi, University of Wisconsin, Madison, United States * Eric Fusy, CNRS/LIX, École Polytechnique, France * Catherine Greenhill, UNSW Sydney, Australia * Brendan McKay, Australian National University, Australia * Bojan Mohar, Simon Fraser University, Canada * Marc Noy, Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Transactions On Information Theory
''IEEE Transactions on Information Theory'' is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society. It covers information theory and the mathematics of communications. It was established in 1953 as ''IRE Transactions on Information Theory''. The editor-in-chief is Muriel Médard (Massachusetts Institute of Technology). As of 2007, the journal allows the posting of preprints on arXiv. According to Jack van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that, among hundreds of computer science-related journals, ''IEEE Transactions on Information Theory'' had the highest ranking and was thus deemed the most prestigious. ''ACM Computing Surveys'', with the highest impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics, Probability And Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás (DPMMS and University of Memphis). History The journal was established by Bollobás in 1992. Fields Medalist Timothy Gowers calls it "a personal favourite" among combinatorics journals and writes that it "maintains a high standard". Content The journal covers combinatorics, probability theory, and theoretical computer science. Currently, it publishes six issues annually. As with other journals from the same publisher, it follows a hybrid green/gold open access policy, in which authors may either place copies of their papers in an institutional repository after a six-month embargo period, or pay an open access charge to make their papers free to read on the journal's website. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete & Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index The Science Citation Index Expanded – previously entitled Science Citation Index – is a citation index originally produced by the Institute for Scientific Information (ISI) and created by Eugene Garfield. It was officially launched in 1964 ...'' * '' Current Contents''/Engineering, Computing and Technology Notable articles The articles by Gil Kalai with a proof of a subexponential upper bound on the diameter of a polyhedron and by Samuel Ferguson on the Kepler conjecture, both published in Discrete & Computational geometry, earned their author the Fulkerson Prize. References Externa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
