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Orbits of the Dissected Polygons of the Generalized Catalan Numbers: Using Burnside's Lemma - Brossura
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Catalan numbers occur regularly throughout many different areas of mathematics. They date back all the way to Euler, and today there are literally hundreds of different realizations of the Catalan number. We can extend the idea of a Catalan number to a generalized Catalan number by adding and extra parameter. In particular, one realization of the generalized Catalan numbers is the number of ways to dissect a regular polygon with (p-1)k+2 sides into k disjoint p+1-gons using (k-1) non-intersecting diagonals. The action of the dihedral group partitions these dissections into some number of orbits. Our main goal of this paper is to find a way to count these orbits for given p and k. In order to do this, we introduce the notion of p-ary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of p-ary trees with k source nodes. Finally, we use Burnside's Lemma as a way to count the number of orbits for a given tree core and extract formulas for the number of orbits for many tree cores that exist for large enough p and k.
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Joseph Auger graduated from the University of Akron where he is presently residing, teaching, and enjoying life in the beautiful Northeast Ohio.
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Orbits of the Dissected Polygons of the Generalized Catalan Numbers
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LAP LAMBERT Academic Publishing Jan 2012, 2012
ISBN 10: 3847339591
ISBN 13: 9783847339595
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Catalan numbers occur regularly throughout many different areas of mathematics. They date back all the way to Euler, and today there are literally hundreds of different realizations of the Catalan number. We can extend the idea of a Catalan number to a generalized Catalan number by adding and extra parameter. In particular, one realization of the generalized Catalan numbers is the number of ways to dissect a regular polygon with (p-1)k+2 sides into k disjoint p+1-gons using (k-1) non-intersecting diagonals. The action of the dihedral group partitions these dissections into some number of orbits. Our main goal of this paper is to find a way to count these orbits for given p and k. In order to do this, we introduce the notion of p-ary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of p-ary trees with k source nodes. Finally, we use Burnside's Lemma as a way to count the number of orbits for a given tree core and extract formulas for the number of orbits for many tree cores that exist for large enough p and k. 92 pp. Englisch. Codice articolo 9783847339595
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Orbits of the Dissected Polygons of the Generalized Catalan Numbers : Using Burnside's Lemma
Editore:
LAP LAMBERT Academic Publishing, 2012
ISBN 10: 3847339591
ISBN 13: 9783847339595
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Da: AHA-BUCH GmbH, Einbeck, Germania
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Catalan numbers occur regularly throughout many different areas of mathematics. They date back all the way to Euler, and today there are literally hundreds of different realizations of the Catalan number. We can extend the idea of a Catalan number to a generalized Catalan number by adding and extra parameter. In particular, one realization of the generalized Catalan numbers is the number of ways to dissect a regular polygon with (p-1)k+2 sides into k disjoint p+1-gons using (k-1) non-intersecting diagonals. The action of the dihedral group partitions these dissections into some number of orbits. Our main goal of this paper is to find a way to count these orbits for given p and k. In order to do this, we introduce the notion of p-ary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of p-ary trees with k source nodes. Finally, we use Burnside's Lemma as a way to count the number of orbits for a given tree core and extract formulas for the number of orbits for many tree cores that exist for large enough p and k. Codice articolo 9783847339595
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Orbits of the Dissected Polygons of the Generalized Catalan Numbers
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LAP LAMBERT Academic Publishing, 2012
ISBN 10: 3847339591
ISBN 13: 9783847339595
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Da: moluna, Greven, Germania
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Auger JosephJoseph Auger graduated from the University of Akron where he is presently residing, teaching, and enjoying life in the beautiful Northeast Ohio.Catalan numbers occur regularly throughout many different areas of mathem. Codice articolo 5511140
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Orbits of the Dissected Polygons of the Generalized Catalan Numbers
Editore:
LAP LAMBERT Academic Publishing Jan 2012, 2012
ISBN 10: 3847339591
ISBN 13: 9783847339595
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Catalan numbers occur regularly throughout many different areas of mathematics. They date back all the way to Euler, and today there are literally hundreds of different realizations of the Catalan number. We can extend the idea of a Catalan number to a generalized Catalan number by adding and extra parameter. In particular, one realization of the generalized Catalan numbers is the number of ways to dissect a regular polygon with (p-1)k+2 sides into k disjoint p+1-gons using (k-1) non-intersecting diagonals. The action of the dihedral group partitions these dissections into some number of orbits. Our main goal of this paper is to find a way to count these orbits for given p and k. In order to do this, we introduce the notion of p-ary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of p-ary trees with k source nodes. Finally, we use Burnside's Lemma as a way to count the number of orbits for a given tree core and extract formulas for the number of orbits for many tree cores that exist for large enough p and k.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 92 pp. Englisch. Codice articolo 9783847339595
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Orbits of the Dissected Polygons of the Generalized Catalan Numbers | Using Burnside's Lemma
Editore:
LAP LAMBERT Academic Publishing, 2012
ISBN 10: 3847339591
ISBN 13: 9783847339595
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Da: preigu, Osnabrück, Germania
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Taschenbuch. Condizione: Neu. Orbits of the Dissected Polygons of the Generalized Catalan Numbers | Using Burnside's Lemma | Joseph Auger | Taschenbuch | 92 S. | Englisch | 2012 | LAP LAMBERT Academic Publishing | EAN 9783847339595 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Codice articolo 106648462
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