Linked Partitions and Linked Cycles

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dc.creatorChen, William Y. C.
dc.creatorWu, Susan Y. J.
dc.creatorYan, Catherine
dc.date2006-07-27
dc.date.accessioned2026-07-07T07:21:04Z
dc.date.available2026-07-07T07:21:04Z
dc.descriptionThe 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 Schroder number $r_n$, which counts the number of Schroder 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.
dc.description22 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/math/0607719
dc.identifierhttp://arxiv.org/abs/math/0607719
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115171
dc.subjectCombinatorics
dc.subject05A15, 05A18
dc.titleLinked Partitions and Linked Cycles
dc.typetext

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