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...
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...
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...
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 ...
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...