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math.CO2013
Linked Partitions and Permutation Tableaux
William Y. C. Chen, Lewis H. Liu, Carol J. Wang
Linked partitions are introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux are introduced by Steingrímsson and Williams in the s…
math.CO2010
Noncrossing Linked Partitions and Large (3,2)-Motzkin Paths
William Y. C. Chen, Carol J. Wang
Noncrossing linked partitions arise in the study of certain transforms in free probability theory. We explore the connection between noncrossing linked partitions and colored Motzk…
math.CO2007
The Limiting Distribution of the Coefficients of the -Catalan Numbers
William Y. C. Chen, Carol J. Wang, Larry X. W. Wang
We show that the limiting distributions of the coefficients of the -Catalan numbers and the generalized -Catalan numbers are normal. Despite the fact that these coefficients…