Orbits of the Dissected Polygons of the Generalized Catalan Numbers

Language: English

Published by LAP LAMBERT Academic Publishing Jan 2012, 2012

3847339591 / 9783847339595

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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.

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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.…

Seller Inventory # 9783847339595

Title
Orbits of the Dissected Polygons of the Generalized Catalan Numbers
Author
Joseph Auger
Publisher
LAP LAMBERT Academic Publishing Jan 2012
Publication year
2012
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3847339591
ISBN 13
9783847339595
Item weight
155 grams
Dimensions
220x150x6 mm

BuchWeltWeit Ludwig Meier e.K.

Bergisch Gladbach, Germany

5-star seller

AbeBooks seller since January 11, 2012

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BuchWeltWeit Ludwig Meier e.K.

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