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Chord Diagram (mathematics)
In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing ( perfect matching) of those objects. Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of 2n cyclically ordered objects is the double factorial (2n-1)!!. There is a Catalan number of chord diagrams on a given ordered set in which no two chords cross each other. The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross. In knot theory, a chord diagram can be used to describe the sequence of crossings along the planar projection of a knot, with each point at which a crossing occurs paired with the point that crosses it. To fully describe the knot, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord Diagrams K6 Matchings
Chord or chords may refer to: Art and music * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord, a chord played on a guitar, which has a particular tuning * The Chords (British band), 1970s British mod revival band * The Chords (American band), 1950s American doo-wop group * ''The Chord'' (painting), a c.1715 painting by Antoine Watteau * Andrew Chord, a comic book character who is the former mentor of the New Warriors Mathematics * Chord (geometry), a line segment joining two points on a curve * Chord (graph theory), an edge joining two nonadjacent nodes in a cycle People * Chord Overstreet, American actor and musician * Chords (musician), a Swedish hiphop/reggae artist Programming * Chord (concurrency), a concurrency construct in some object-oriented programming languages * Chord (peer-to-peer), a peer-to-peer protocol and algorithm for distributed hash tables (DHT) Science and technology * Chord (astronomy), a line crossin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss Diagram
Gauss notation (also known as a Gauss code or Gauss words) is a notation for mathematical knots. It is created by enumerating and classifying the crossings of an embedding of the knot in a plane. It is named after the German mathematician Carl Friedrich Gauss (1777–1855). Gauss code represents a knot with a sequence of integers. However, rather than every crossing being represented by two different numbers, crossings are labelled with only one number. When the crossing is an overcrossing, a positive number is listed. At an undercrossing, a negative number. For example, the trefoil knot in Gauss code can be given as: 1,−2,3,−1,2,−3. Gauss code is limited in its ability to identify knots by a few problems. The starting point on the knot at which to begin tracing the crossings is arbitrary, and there is no way to determine which direction to trace in. Also, the Gauss code is unable to indicate the handedness of each crossing, which is necessary to identify a knot versus its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Mathematics Research Notices
The ''International Mathematics Research Notices'' is a peer-reviewed mathematics journal. Originally published by Duke University Press and Hindawi Publishing Corporation, it is now published by Oxford University Press. retrieved 2015-02-26. The Executive Editor is (). According to the '' |
European Journal Of Combinatorics
The ''European Journal of Combinatorics'' is an international peer-reviewed scientific journal that specializes in combinatorics. The journal primarily publishes papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and the theories of computing. The journal includes full-length research papers, short notes, and research problems on several topics. This journal has been founded in 1980 by Michel Deza, Michel Las Vergnas and Pierre Rosenstiehl. The current editor-in-chief is Patrice Ossona de Mendez and the vice editor-in-chief is Marthe Bonamy. Abstracting and indexing The journal is abstracted and indexed in *MathSciNet, *Science Citation Index Expanded, *Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Statistical Planning And Inference
The ''Journal of Statistical Planning and Inference'' is a monthly peer-reviewed scientific journal covering research on statistical inference. The editors-in-chief are A. DasGupta, H. Dette and W.-L. Loh. The journal was established in 1977. According to the ''Journal Citation Reports'', the journal has a 2012 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 0.713. References External links * Statistics journals Academic journals established in 1977 Monthly journals English-language journals Elsevier academic journals {{statistics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kontsevich Invariant
In the knot theory, mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link (knot theory), link, is a Finite type invariant#The universal Vassiliev invariant, universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type invariant, finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients. It was defined by Maxim Kontsevich. The Kontsevich invariant is a universal quantum invariant in the sense that any quantum invariant may be recovered by substituting the appropriate #Weight system, weight system into any #Jacobi diagram and Chord diagram, Jacobi diagram. Definition The Kontsevich invariant is defined by monodromy along solutions of the Knizhnik–Zamolodchikov equations. Jacobi diagram and Chord diagram Definition Let be a circle (which is a 1-dimensional manifold). As is shown in the figure on the ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
