Linked partitions and linked cycles Academic Article uri icon

abstract

  • The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n + 1] is equal to the n-th large Schrder number rn, which counts the number of Schrder paths. In this paper we give a bijective proof of this result. Then we introduce the structures of linked partitions and linked cycles. We present various combinatorial properties of noncrossing linked partitions, linked partitions, and linked cycles, and connect them to other combinatorial structures and results, including increasing trees, partial matchings, k-Stirling numbers of the second kind, and the symmetry between crossings and nestings over certain linear graphs. 2007 Elsevier Ltd. All rights reserved.

published proceedings

  • EUROPEAN JOURNAL OF COMBINATORICS

author list (cited authors)

  • Chen, W., Wu, S., & Yan, C. H.

citation count

  • 15

complete list of authors

  • Chen, William YC||Wu, Susan YJ||Yan, Catherine H

publication date

  • January 2008