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Linked Partitions and Linked Cycles by William Y.C. Chen; Susan Y.J. Wu; Catherine H. Yan is a Mathematics article available to read on EtoBox.

What is Linked Partitions and Linked Cycles about?

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 Schröder number r n , which counts the number of Schröder 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.

Who reads Linked Partitions and Linked Cycles?

Author

William Y.C. Chen; Susan Y.J. Wu; Catherine H. Yan

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0195-6698)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)