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math.CO2008
Klazar trees and perfect matchings
David Callan
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w_{12}, led to a recurrence r…
math.CO2008
Circular Digraph Walks, k-Balanced Strings, Lattice Paths and Chebychev Polynomials
Evangelos Georgiadis, David Callan, Qing-Hu Hou
We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves…
math.CO2008
Pattern avoidance in "flattened" partitions
David Callan
To flatten a set partition (with apologies to Mathematica) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks a…