mathematics, the Prüfer sequence (also Prüfer code or Prüfer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree...
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named after him: Prüfer sequence (also known as a Prüfer code; it has broad applications in graph theory and network theory). Prüfer domain. Also see...
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of each tree. Any tree can be uniquely encoded into a Prüfer sequence, and any Prüfer sequence can be uniquely decoded into a tree; these two results...
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groups. The groups are named after Heinz Prüfer, a German mathematician of the early 20th century. The Prüfer p-group may be identified with the subgroup...
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Genome (redirect from Genomic sequence)
December 2013. Prüfer K, Racimo F, Patterson N, Jay F, Sankararaman S, Sawyer S, et al. (January 2014). "The complete genome sequence of a Neanderthal...
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kind of tree. As with any tree, stars may be encoded by a Prüfer sequence; the Prüfer sequence for a star K1,k consists of k − 1 copies of the center vertex...
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List of algorithms (redirect from List of sequence algorithms)
algorithm for finding a perfect matching Prüfer coding: conversion between a labeled tree and its Prüfer sequence Tarjan's off-line lowest common ancestors...
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trees in an arbitrary graph involving the determinant of a matrix. Prüfer sequences yield a bijective proof of Cayley's formula. Another bijective proof...
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most classical examples of bijective proofs in combinatorics include: Prüfer sequence, giving a proof of Cayley's formula for the number of labeled trees...
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Mandelbrot set (redirect from Mandelbrot sequence)
Exhibition of the Goethe-Institut by H.O. Peitgen, P. Richter, H. Jürgens, M. Prüfer, D.Saupe. Since 1985 shown in over 40 countries. Gleick, James (1987). Chaos:...
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trees BEST theorem Markov chain tree theorem Minimum spanning tree Prüfer sequence O'Toole, J.B. (1958). "On the Solution of the Equations Obtained from...
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In mathematics, two Prüfer theorems, named after Heinz Prüfer, describe the structure of certain infinite abelian groups. They have been generalized by...
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Pure submodule (redirect from Pure exact sequence)
modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave short exact sequences exact after tensoring...
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that there are nn−2 trees on n labeled vertices. A classic proof uses Prüfer sequences, which naturally show a stronger result: the number of trees with vertices...
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1188021. PMC 5100745. PMID 20448178. Reich 2018. Prüfer, K.; et al. (2014). "The complete genome sequence of a Neanderthal from the Altai Mountains". Nature...
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Partitions Subsets Permutation group: Polyhedral, Rubik, Symmetric, etc. Prufer sequence and Gray codes Pretty-printing: ASCII/Unicode pretty-printing, LaTeX...
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October 2014). "45,000-Year-Old Man's Genome Sequenced". Scientific American. Retrieved 24 October 2014. Prüfer, Kay; Posth, Cosimo; Yu, He; Stoessel, Alexander;...
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with later Eurasians); Fumane 2, c. 40,000 BP. Prüfer, Kay; Posth, Cosimo (June 2021). "A genome sequence from a modern human skull over 45,000 years old...
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Gansauge M, Benazzi S, Sawyer S, Hublin J, Shunkov MV, Derevianko AP, Kelso J, Prüfer K, Meyer M, Pääbo S (July 2017). "A fourth Denisovan individual". Science...
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PMC 3144383. Prüfer, K.; Racimo, F.; Patterson, N.; Jay, F.; Sankararaman, S.; Sawyer, S.; et al. (2014) [Online 2013]. "The complete genome sequence of a Neanderthal...
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PMID 30135540. Prüfer, K.; Racimo, Fernando; Patterson, N.; Jay, F.; Sankararaman, S.; Sawyer, S.; et al. (2013). "The complete genome sequence of a Neanderthal...
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PMID 20448178. Prüfer, K.; Racimo, F.; Patterson, N.; Jay, F.; Sankararaman, S.; Sawyer, S.; et al. (2014) [Online 2013]. "The complete genome sequence of a Neanderthal...
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PMID 31488661. Prüfer, Kay; Racimo, Fernando; Patterson, Nick; Jay, Flora; Reich, David; Pääbo, Svante (2014-01-02). "The complete genome sequence of a Neanderthal...
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Bibcode:2005Natur.437...69.. doi:10.1038/nature04072. PMID 16136131. S2CID 2638825. Prüfer K, Munch K, Hellmann I, Akagi K, Miller JR, Walenz B, et al. (June 2012)...
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original on 1 January 2012. Retrieved 22 December 2010. Prüfer, Kay (2013). "The complete genome sequence of a Neanderthal from the Altai Mountains". Nature...
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taken from Vindija 33.16, Vindija 33.25 and Vindija 33.26. Prüfer et al. (2017) sequenced a high coverage genome from Vindija 33.19. At around 30-fold...
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Pentominoes Tetrominoes Polysquare puzzle Projective plane Property B Prüfer sequence q-analog q-binomial theorem—see Gaussian binomial coefficient q-derivative...
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J, Pääbo S. A high-coverage genome sequence from an archaic Denisovan individual. Science. 2012:338:222-226. Prüfer K, Racimo F, Patterson N, Jay F, Sankararaman...
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the Czech Republic. Retrieved 8 September 2010. Prüfer, Kay; Posth, Cosimo (June 2021). "A genome sequence from a modern human skull over 45,000 years old...
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In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank...
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