Orbits of the Dissected Polygons of the Generalized Catalan Numbers
für 44.10€ kaufen ··· 9783847339595 ··· 10361496 ··· 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. Hersteller: LAP Lambert Academic Publishing Marke: LAP Lambert Academic Publishing EAN: 9783847339595 Kat: Hardcover/Naturwissenschaften, Medizin, Informatik, Technik/Mathematik Lieferzeit: Sofort lieferbar Versandkosten: Ab 20¤ Versandkostenfrei in Deutschland Icon: https://www.inforius-bilder.de/bild/?I=UfXCAj4BcF%2F8PBTgMwWmsY2Dqx7owZVYIewmW2vQaDQ%3D Bild:
Affiliate Marketing
AdHoc MeldungenAffiliate & PublisherAdvertiser & MerchantAcademyAntwortenArtikelsucheAdventskalender
AffilitivProduktdatenPreisvergleich
