67 search results - page 1 / 14 » Divisibility of generalized Catalan numbers |
63
Voted
JCT
2007
14 years 10 months ago
2007
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...
DM
2008
14 years 10 months ago
2008
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...
78
Voted
JCT
2007
14 years 10 months ago
2007
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...
80
Voted
ARSCOM
2008
14 years 10 months ago
2008
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 ...
JCT
2011
14 years 5 months ago
2011
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 ....