Orbits of the Dissected Polygons of the Generalized Catalan Numbers: Using Burnside's Lemma,Used

Orbits of the Dissected Polygons of the Generalized Catalan Numbers: Using Burnside's Lemma,Used

In Stock
SKU: DADAX3847339591
Brand: LAP Lambert Academic Publishing
$81.01 $115.73
Save $34.72
Quantity
Add to wishlist
Add to compare

Processing time: 1-3 days

US Orders Ships in: 3-5 days

International Orders Ships in: 8-12 days

Return Policy: 15-days return on defective items

Payment Option
Payment Methods

Help

If you have any questions, you are always welcome to contact us. We'll get back to you as soon as possible, withing 24 hours on weekdays.

Customer service

All questions about your order, return and delivery must be sent to our customer service team by e-mail at yourstore@yourdomain.com

Sale & Press

If you are interested in selling our products, need more information about our brand or wish to make a collaboration, please contact us at press@yourdomain.com

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 (p1)k+2 sides into k disjoint p+1gons using (k1) nonintersecting 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 pary trees. We show that the number of diagonalizations of our polygon is equivalent to the number of pary 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.

⚠️ WARNING (California Proposition 65):

This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.

For more information, please visit www.P65Warnings.ca.gov.

Recently Viewed