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Enumerations Of Specific Permutation Classes
In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively few basis elements. This area of study has turned up unexpected instances of Wilf equivalence, where two seemingly-unrelated permutation classes have the same numbers of permutations of each length. Classes avoiding one pattern of length 3 There are two symmetry classes and a single Wilf class for single permutations of length three. Classes avoiding one pattern of length 4 There are seven symmetry classes and three Wilf classes for single permutations of length four. No non-recursive formula counting 1324-avoiding permutations is known. A recursive formula was given by . A more efficient algorithm using functional equations was given by , which was enhanced by , and then further enhanced by who give the first 50 terms of the enumeration. have provided lower and upper bounds for the growth of this class. Classes avo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of digits representing the result of applying the permutation to the digit sequence 123...; for instance the digit sequence 213 represents the permutation on three elements that swaps elements 1 and 2. If π and σ are two permutations represented in this way (these variable names are standard for permutations and are unrelated to the number pi), then π is said to ''contain'' σ as a ''pattern'' if some subsequence of the digits of π has the same relative order as all of the digits of σ. For instance, permutation π contains the pattern 213 whenever π has three digits ''x'', ''y'', and ''z'' that appear within π in the order ''x''...''y''...''z'' but whose values are ordered as ''y'' < ''x'' < ''z'', the same as the ordering of the values in the permutation 213. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew-merged Permutation
In the theory of permutation patterns, a skew-merged permutation is a permutation that can be partitioned into an increasing sequence and a decreasing sequence. They were first studied by and given their name by . Characterization The two smallest permutations that cannot be partitioned into an increasing and a decreasing sequence are 3412 and 2143. was the first to establish that a skew-merged permutation can also be equivalently defined as a permutation that avoids the two patterns 3412 and 2143. A permutation is skew-merged if and only if its associated permutation graph is a split graph, a graph that can be partitioned into a clique (corresponding to the descending subsequence) and an independent set (corresponding to the ascending subsequence). The two forbidden patterns for skew-merged permutations, 3412 and 2143, correspond to two of the three forbidden induced subgraphs for split graphs, a four-vertex cycle and a graph with two disjoint edges, respectively. The third forb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Journal Of Mathematics
European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe and other Western countries * ''European'', an adjective referring to something of, from, or related to the European Union ** Citizenship of the European Union ** Demographics of the European Union In publishing * ''The European'' (1953 magazine), a far-right cultural and political magazine published 1953–1959 * ''The European'' (newspaper), a British weekly newspaper published 1990–1998 * ''The European'' (2009 magazine), a German magazine first published in September 2009 *''The European Magazine'', a magazine published in London 1782–1826 *''The New European'', a British weekly pop-up newspaper first published in July 2016 Other uses * * Europeans (band), a British post-punk group, from Bristol See also * * * Europe (disam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics & Theoretical Computer Science
''Discrete Mathematics & Theoretical Computer Science'' is a peer-reviewed open access scientific journal covering discrete mathematics and theoretical computer science. It was established in 1997 by Daniel Krob (Paris Diderot University). Since 2001, the editor-in-chief is Jens Gustedt (Institut National de Recherche en Informatique et en Automatique). Abstracting and indexing The journal is abstracted and indexed in ''Mathematical Reviews'' and the Science Citation Index Expanded. According to the ''Journal Citation Reports'', the journal has a 2011 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 citations of articles published in the last two years in a given journal, as i ... of 0.465. References External links * {{DEFAULTSORT:Discrete Mathematics and Theoretical Computer Science Combinatorics journals Computer science journals Pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
European Journal Of Combinatorics
European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe and other Western countries * ''European'', an adjective referring to something of, from, or related to the European Union ** Citizenship of the European Union ** Demographics of the European Union In publishing * ''The European'' (1953 magazine), a far-right cultural and political magazine published 1953–1959 * ''The European'' (newspaper), a British weekly newspaper published 1990–1998 * ''The European'' (2009 magazine), a German magazine first published in September 2009 *''The European Magazine'', a magazine published in London 1782–1826 *''The New European'', a British weekly pop-up newspaper first published in July 2016 Other uses * * Europeans (band), a British post-punk group, from Bristol See also * * * Europe (disam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory, Series A
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, |
Australasian Journal Of Combinatorics
The ''Australasian Journal of Combinatorics'' is a triannual peer-reviewed open-access scientific journal covering combinatorics. It was established in 1990 and is published by the Centre for Discrete Mathematics and Computing (University of Queensland) on behalf of the Combinatorial Mathematics Society of Australasia. Originally published biannually, it has been published three times per year since 2005. The editors-in-chief are Michael H. Albert (University of Otago) and Elizabeth J. Billington (University of Queensland). Since 2014, the journal has been diamond open access, charging fees neither to readers nor to authors. Abstracting and indexing The journal is abstracted and indexed in ''Mathematical Reviews'', the Emerging Sources Citation Index, Scopus, and ''Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – ... [...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, Universitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Mathematics And Applications
Pure may refer to: Computing * A pure function * A pure virtual function * PureSystems, a family of computer systems introduced by IBM in 2012 * Pure Software, a company founded in 1991 by Reed Hastings to support the Purify tool * Pure-FTPd, FTP server software * Pure (programming language), functional programming language based on term rewriting * Pure Storage, a company that makes datacenter storage solutions * Pure (CRIS), a research information system bought by Elsevier. Companies and products * Pure (app), dating app * Pure (restaurant chain), a British fast food chain * Pure Insurance, Privilege Underwriters Reciprocal Exchange * Pure Trading, a Canadian electronic communication network operated by CNQ * Pure Digital, a UK consumer electronics company specialising in DAB radios * Pure Oil, a U.S. chain of gas stations * Propulsion Universelle et Récuperation d'Énergie (PURE), a motorsport engineering company * Pure FM (Portsmouth), a university radio station based ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advances In Applied Mathematics
''Advances in Applied Mathematics'' is a peer-reviewed mathematics journal publishing research on applied mathematics. Its founding editor was Gian-Carlo Rota (Massachusetts Institute of Technology); from 1980 to 1999, Joseph P. S. Kung (University of North Texas) served as managing editor. It is currently published by Elsevier with eight issues per year and edited by Hal Schenck (Auburn University) and Catherine Yan (Texas A&M University). Abstracting and indexing The journal is abstracted and indexed by: * ACM Guide to Computing Literature * CompuMath Citation Index * Current Contents/Physics, Chemical, & Earth Sciences * ''Mathematical Reviews'' * Science Citation Index * Scopus According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.848. See also * List of periodicals published by Elsevier This is a list of scientific, technical and general interest periodicals published by Elsevier or one of its imprints or subsidiary companies. Both pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riffle Shuffle Permutation
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n items that can be obtained by a single riffle shuffle, in which a sorted deck of n cards is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top of the sorted deck). Beginning with an ordered set (1 rising sequence), mathematically a riffle shuffle is defined as a permutation on this set containing 1 or 2 rising sequences. The permutations with 1 rising sequence are the identity permutations. As a special case of this, a (p,q)-shuffle, for numbers p and q with p+q=n, is a riffle in which the first packet has p cards and the second packet has q cards.Weibel, Charles (1994). ''An Introduction to Homological Algebra'', p. 181. Cambridge University Press, Cambridge. Combinatorial enumeration Since a (p,q)-shuffle is completely determined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
