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» Divisibility of generalized Catalan numbers
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63
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JCT
2007
71views more  JCT 2007»
14 years 10 months ago
Divisibility of generalized Catalan numbers
We define a q generalization of weighted Catalan numbers studied by Postnikov and Sagan, and prove a result on the divisibility by p of such numbers when p is a prime and q its p...
Matjaz Konvalinka
DM
2008
100views more  DM 2008»
14 years 10 months ago
Staircase tilings and k-Catalan structures
Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible generalization of the Catalan numbers. We will present a new combinatorial object that...
Silvia Heubach, Nelson Y. Li, Toufik Mansour
78
Voted
JCT
2007
97views more  JCT 2007»
14 years 10 months ago
What power of two divides a weighted Catalan number?
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...
Alexander Postnikov, Bruce E. Sagan
80
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ARSCOM
2008
118views more  ARSCOM 2008»
14 years 10 months ago
Proper Partitions of a Polygon and k-Catalan Numbers
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1, 2, . . . , c. Motivated by conjectures of Propp, we are led to consider partitions of ...
Bruce E. Sagan
JCT
2011
66views more  JCT 2011»
14 years 5 months ago
Enumeration of non-crossing pairings on bit strings
A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings 1n1 0m1 ....
Todd Kemp, Karl Mahlburg, Amarpreet Rattan, Cliffo...