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| [[File:Cremona-Richmond configuration.svg|thumb|240px|The Cremona–Richmond configuration]]
| | Single Premium Life Insurance Policy<br>Deezer , comme tous les services de ce kind, nécessite un abonnement premium pour pouvoir être utilisé sans limite. The French music-streaming service is crossing the Atlantic with a little support from premium wireless speaker enterprise Sonos. Peachtree premium has a far better presentation attributes which make presents the reports of rapid promoting and slow promoting items to give a clear image of the existing company position. Your driving history: It is a single of the major components in establishing your car premium. For example, if you have a clean record with no accident history you can get discounts upto 50% on your auto insurance premium by the way of No Claim Bonus. SMS alerts are also yet another feature of Premium SMS.<br><br>Pour toute nouvelle acquisition à partir du 2 octobre, [http://deezerpremiumgratuitement.com compte deezer premium] sera en promotion au tarif de 1€ pendant six mois avant de repasser au tarif habituel de 9€99/mois. Nous avons joints Orange à ce sujet mais, à l'heure actuelle, ils ne peuvent pas nous répondre mais nous signalent néanmoins que des discussions sont en cours entre les deux entreprises pour renouveler le contrat. En revanche, le logiciel Spotify est plus intuitif que Deezer.<br><br>Cet accord est une opportunité exceptionnelle pour Deezer qui s'appuiera sur le nombre énorme de membres du réseau social pour faire connaitre son service, notamment à l'international. Grâce à un autre partenariat avec Philips, l'application Deezer est directement disponible sur les enceintes Fidelio de la marque. De l'autre côté, Philips pourra tenter de vendre ses produits directement sur le web page [http://deezerpremiumgratuitement.com compte deezer premium+ gratuit] Deezer. On dirait que vous faite l'éloge de Deezer ici.<br><br>J'ai un compte gratuit etc… Le problème est que quand je veux écouter de la musique (ma playlist par exemple) Deezer me déplace à la web page « musique à la demande, réservé aux abonnés premium + » ! J'ai acheté une carte deezer 20 € mais elle ne marche pas des que je rentre le code elle me dit que j'ai les avantage gratuit et non payant comme promis sur la carte je trouve sa scandaleux ! Automobile Model/Sort: The new car demands far more premium.<br><br>Pour info (un peu tardive), j'ai un abonnement Deezer à four,99€ et ça suffit pour bénéficier de toutes les fonctionnalités Sonos avec l'iPad et l'iPhone. Après une année d'existence, WorMee n'a jamais profité de la puissance commerciale du groupe et ne réunissait que 700 000 visiteurs par mois soit 10 fois moins que Deezer. Deezer ne dispose pas d'un numéro de téléphone de contact pour son service client.Deezer a besoin d'élargir sa base grâce à un opérateur capable de commercialiser ses offres payantes (Deezer Premium à 4 [http://deezerpremiumgratuitement.com deezer premium+ gratuit].99€/mois ou Deezer Premium+ à 9.99€) auprès de plusieurs millions de consumers. Ainsi, malgré 7 millions de visiteurs chaque mois, Deezer ne compte que 25 000 abonnements Premium. L'objectif est donc d'améliorer la rentabilité du service en transformant un maximum de clients Orange en abonnés Deezer. |
| In mathematics, the '''Cremona–Richmond configuration''' is a [[configuration (geometry)|configuration]] of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no triangles. It was studied by {{harvs|txt|last=Cremona|year=1877|authorlink=Luigi Cremona}} and {{harvs|txt|last=Richmond|year=1900|authorlink=Herbert William Richmond}}. It is a [[generalized quadrangle]] with parameters (2,2). Its [[Levi graph]] is the [[Tutte–Coxeter graph]].<ref name="cc"/>
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| ==Symmetry==
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| The points of the Cremona–Richmond configuration may be identified with the <math>15=\binom{6}{2}</math> unordered pairs of elements of a six-element set, and the lines of the configuration may be identified with the 15 ways of partitioning the same six elements into three pairs, in such a way that a point is incident to a line if and only if the corresponding pair of elements is one of the pairs in the corresponding partition. In this scheme, the pairs of elements are called duads and the partitions into three pairs are called synthemes. In this way, the [[symmetric group]] on six elements may be seen to act transitively on the flags of the configuration, where a flag is an incident point-line pair. This group is the [[automorphism]] group of the configuration.<ref name="cc">{{harvtxt|Coxeter|1950}}; {{harvtxt|Coxeter|1958}}. The terminology of duads and synthemes is from {{harvtxt|Sylvester|1844}}, but Sylvester treats these systems of pairs and partitions in the context of a more general study of tuples and partitions of sets, does not reserve special attention to the case of a six-element set, and does not associate any geometric meaning to the sets.</ref> | |
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| The Cremona–Richmond configuration is [[Duality (projective geometry)|self-dual]]: it is possible to exchange points for lines while preserving all the incidences of the configuration. This duality gives the Tutte–Coxeter graph additional symmetries beyond those of the Cremona–Richmond configuration, which swap the two sides of its bipartition. These symmetries correspond to the [[outer automorphism]]s of the symmetric group on six elements.
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| ==Realization==
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| Any six points in general position in four-dimensional space determine 15 points where a line through two of the points intersects the [[hyperplane]] through the other four points; thus, the duads of the six points correspond one-for-one with these 15 derived points.
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| Any three duads that together form a syntheme determine a line, the intersection line of the three hyperplanes containing two of the three duads in the syntheme, and this line contains each of the points derived from its three duads. Thus, the duads and synthemes of the abstract configuration correspond one-for-one, in an incidence-preserving way, with these 15 points and 15 lines derived from the original six points, which form a realization of the configuration. The same realization may be projected into Euclidean space or the Euclidean plane.<ref name="cc"/>
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| The Cremona–Richmond configuration also has a one-parameter family of realizations in the plane with order-five cyclic symmetry.<ref>{{harvtxt|Zacharias|1951}}; {{harvtxt|Boben|Pisanski|2003}}; {{harvtxt|Boben|Grünbaum|Pisanski|Žitnik|2006}}.</ref>
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| ==History==
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| {{harvs|txt|last=Schläfli|first=Ludwig|authorlink=Ludwig Schläfli|year=1858|year2=1863}} found [[cubic surface]]s containing sets of 15 real lines (complementary to a [[Schläfli double six]] in the set of all 27 lines on a cubic) and 15 tangent planes, with three lines in each plane and three planes through each line. Intersecting these lines and planes by another plane results in a 15<sub>3</sub>15<sub>3</sub> configuration. The specific incidence pattern of Schläfli's lines and planes was later published by {{harvs|txt|last=Cremona|first=Luigi|year=1868|authorlink=Luigi Cremona}}. The observation that the resulting configuration contains no triangles was made by {{harvtxt|Martinetti|1886}}, and the same configuration also appears in the work of {{harvs|txt|first=Herbert William|last=Richmond|authorlink=Herbert William Richmond|year=1900}}. {{harvtxt|Visconti|1916}} found a description of the configuration as a self-inscribed polygon. [[H. F. Baker]] used the four-dimensional realization of this configuration as the frontispiece for two volumes of his 1922–1925 textbook, ''Principles of Geometry''. {{harvtxt|Zacharias|1951}} also rediscovered the same configuration, and found a realization of it with order-five cyclic symmetry.<ref name="bgpz">This history and most of the references in it are drawn from {{harvtxt|Boben|Grünbaum|Pisanski|Žitnik|2006}}. The reference to Baker is from {{harvtxt|Coxeter|1950}}.</ref>
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| The name of the configuration comes from the studies of it by {{harvs|last=Cremona|year=1868|year2=1877|txt}} and {{harvtxt|Richmond|1900}}; perhaps due to some mistakes in his work, the contemporaneous contribution of Martinetti fell into obscurity.<ref name="bgpz"/>
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| ==Notes==
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| {{reflist}}
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| ==References==
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| *{{citation
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| | last1 = Boben | first1 = M. | |
| | last2 = Pisanski | first2 = T. | author2-link = Tomaž Pisanski | |
| | doi = 10.1016/S0195-6698(03)00031-3
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| | issue = 4
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| | journal = European Journal of Combinatorics
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| | mr = 1975946
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| | pages = 431–457
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| | title = Polycyclic configurations
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| | url = http://www.imfm.si/preprinti/PDF/00770.pdf
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| | volume = 24
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| | year = 2003}}
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| *{{citation
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| | last1 = Boben | first1 = Marko
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| | last2 = Grünbaum | first2 = Branko | author2-link = Branko Grünbaum
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| | last3 = Pisanski | first3 = Tomaž | author3-link = Tomaž Pisanski
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| | last4 = Žitnik | first4 = Arjana
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| | doi = 10.1007/s00454-005-1224-9
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| | issue = 3
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| | journal = [[Discrete and Computational Geometry]]
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| | mr = 2202110
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| | pages = 405–427
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| | title = Small triangle-free configurations of points and lines
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| | url = http://www.imfm.si/preprinti/PDF/00938.pdf
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| | volume = 35 | |
| | year = 2006}}.
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| *{{citation
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| | last = Coxeter | first = H. S. M. | author-link = Harold Scott MacDonald Coxeter
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| | doi = 10.1090/S0002-9904-1950-09407-5
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| | journal = Bulletin of the American Mathematical Society
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| | mr = 0038078
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| | pages = 413–455
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| | title = Self-dual configurations and regular graphs
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| | volume = 56
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| | year = 1950}}.
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| *{{cite journal
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| | last = Coxeter | first = H. S. M. | author-link = Harold Scott MacDonald Coxeter
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| | title = Twelve points in PG(5,3) with 95040 self-transformations
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| | journal = [[Proceedings of the Royal Society A]] | |
| | volume = 247
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| | year = 1958
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| | issue = 1250
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| | pages = 279–293
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| | jstor = 100667
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| | doi = 10.1098/rspa.1958.0184}}.
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| *{{citation
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| | last = Cremona | first = L. | authorlink = Luigi Cremona
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| | journal = J. Reine Angew. Math.
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| | pages = 1–133
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| | title = Mémoire de géométrie pure sur les surfaces du troisieme ordre
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| | volume = 68
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| | year = 1868}}. As cited by {{harvtxt|Boben|Grünbaum|Pisanski|Žitnik|2006}}.
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| *{{Citation | last1=Cremona | first1=L. | authorlink = Luigi Cremona | title=Teoremi stereometrici dal quali si deducono le proprietà dell' esagrammo di Pascal | url=http://books.google.com/books?id=FoYlSQAACAAJ | series=Atti della R. Accademia dei Lincei | year=1877 | volume=1}}
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| *{{Citation | last1=Grünbaum | first1=Branko | author1-link=Branko Grünbaum | title=Configurations of points and lines | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=Graduate Studies in Mathematics | isbn=978-0-8218-4308-6 | mr=2510707 | year=2009 | volume=103}}
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| *{{citation
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| | last = Martinetti | first = V.
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| | doi = 10.1007/BF02420733
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| | issue = 1
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| | journal = Annali di matematica pura ed applicata | series = (2)
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| | pages = 161–192
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| | title = Sopra alcune configurazioni piane
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| | volume = 14
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| | year = 1886}}.
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| *{{Citation | last1=Richmond | first1=H. W. |authorlink=Herbert William Richmond| title=On the figure of six points in space of four dimensions. | url=http://resolver.sub.uni-goettingen.de/purl?PPN600494829_0031 | year=1900 | journal=Quart. J. | volume=31 | pages=125–160}}
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| *{{citation
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| | last = Schläfli | first = L. | author-link = Ludwig Schläfli | |
| | journal = Quart. J. Pure Appl. Math.
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| | pages = 55–65, 110–120
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| | title = An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface
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| | url = http://resolver.sub.uni-goettingen.de/purl?PPN600494829_0002
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| | volume = 2
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| | year = 1858}}.
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| *{{citation
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| | last = Schläfli | first = L. | author-link = Ludwig Schläfli | |
| | doi = 10.1098/rstl.1863.0010
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| | journal = Philosophical Transactions of the Royal Society
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| | pages = 193–241
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| | title = On the distribution of surfaces of the third order into species, in reference to the absence or presence of singular points, and the reality of their lines
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| | url = http://archive.org/details/philtrans03162110
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| | volume = 153 | |
| | year = 1863}}.
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| *{{cite journal
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| | author = Sylvester, J. J.
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| | authorlink = J. J. Sylvester
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| | title = Elementary researches in the analysis of combinatorial aggregation
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| | journal = The Philos. Mag. | series = Series 3
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| | volume = 24
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| | year = 1844
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| | pages = 285–295}}.
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| *{{citation
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| | last = Visconti | first = E.
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| | journal = Giornale di Matematiche di Battaglini
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| | pages = 27–41
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| | title = Sulle configurazioni piane atrigone
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| | volume = 54
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| | year = 1916}}. As cited by {{harvtxt|Boben|Grünbaum|Pisanski|Žitnik|2006}}.
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| *{{citation
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| | last = Zacharias | first = Max
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| | doi = 10.1002/mana.19510050602
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| | journal = [[Mathematische Nachrichten]]
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| | mr = 0043473
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| | pages = 329–345
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| | title = Streifzüge im Reich der Konfigurationen: Eine Reyesche Konfiguration (15<sub>3</sub>), Stern- und Kettenkonfigurationen
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| | volume = 5
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| | year = 1951}}.
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| ==External links==
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| *{{mathworld|title=Cremona–Richmond Configuration|urlname=Cremona-RichmondConfiguration}}
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| *[http://archive.org/stream/principlesofgeom04bake#page/n7/mode/2up Image ofCremona–Richmond configuration]
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| *[http://archive.org/stream/principlesofgeom02bake#page/n7/mode/2up Image ofCremona–Richmond configuration]
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| {{DEFAULTSORT:Cremona-Richmond configuration}}
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| [[Category:Configurations]]
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Single Premium Life Insurance Policy
Deezer , comme tous les services de ce kind, nécessite un abonnement premium pour pouvoir être utilisé sans limite. The French music-streaming service is crossing the Atlantic with a little support from premium wireless speaker enterprise Sonos. Peachtree premium has a far better presentation attributes which make presents the reports of rapid promoting and slow promoting items to give a clear image of the existing company position. Your driving history: It is a single of the major components in establishing your car premium. For example, if you have a clean record with no accident history you can get discounts upto 50% on your auto insurance premium by the way of No Claim Bonus. SMS alerts are also yet another feature of Premium SMS.
Pour toute nouvelle acquisition à partir du 2 octobre, compte deezer premium sera en promotion au tarif de 1€ pendant six mois avant de repasser au tarif habituel de 9€99/mois. Nous avons joints Orange à ce sujet mais, à l'heure actuelle, ils ne peuvent pas nous répondre mais nous signalent néanmoins que des discussions sont en cours entre les deux entreprises pour renouveler le contrat. En revanche, le logiciel Spotify est plus intuitif que Deezer.
Cet accord est une opportunité exceptionnelle pour Deezer qui s'appuiera sur le nombre énorme de membres du réseau social pour faire connaitre son service, notamment à l'international. Grâce à un autre partenariat avec Philips, l'application Deezer est directement disponible sur les enceintes Fidelio de la marque. De l'autre côté, Philips pourra tenter de vendre ses produits directement sur le web page compte deezer premium+ gratuit Deezer. On dirait que vous faite l'éloge de Deezer ici.
J'ai un compte gratuit etc… Le problème est que quand je veux écouter de la musique (ma playlist par exemple) Deezer me déplace à la web page « musique à la demande, réservé aux abonnés premium + » ! J'ai acheté une carte deezer 20 € mais elle ne marche pas des que je rentre le code elle me dit que j'ai les avantage gratuit et non payant comme promis sur la carte je trouve sa scandaleux ! Automobile Model/Sort: The new car demands far more premium.
Pour info (un peu tardive), j'ai un abonnement Deezer à four,99€ et ça suffit pour bénéficier de toutes les fonctionnalités Sonos avec l'iPad et l'iPhone. Après une année d'existence, WorMee n'a jamais profité de la puissance commerciale du groupe et ne réunissait que 700 000 visiteurs par mois soit 10 fois moins que Deezer. Deezer ne dispose pas d'un numéro de téléphone de contact pour son service client.Deezer a besoin d'élargir sa base grâce à un opérateur capable de commercialiser ses offres payantes (Deezer Premium à 4 deezer premium+ gratuit.99€/mois ou Deezer Premium+ à 9.99€) auprès de plusieurs millions de consumers. Ainsi, malgré 7 millions de visiteurs chaque mois, Deezer ne compte que 25 000 abonnements Premium. L'objectif est donc d'améliorer la rentabilité du service en transformant un maximum de clients Orange en abonnés Deezer.