@Article{CMR-35-1,
author = {Wenkui, Guo and Niu, Feifei},
title = {Singly Covered Minimal Elements of Linked Partitions and Cycles of Permutations},
journal = {Communications in Mathematical Research },
year = {2019},
volume = {35},
number = {1},
pages = {75--80},
abstract = {<p style="text-align: justify;">Linked partitions were introduced by Dykema (Dykema K J. Multilinear function series and transforms in free probability theory. $Adv$. $Math$., 2005, 208(1): 351–407) in the study of the unsymmetrized T-transform in free probability theory. Permutation is one of the most classical combinatorial structures. According to the linear representation of linked partitions, Chen $et$ $al$. (Chen W Y C, Wu S Y J, Yan C H. Linked partitions and linked cycles. $European$ $J$. $Combin$., 2008, 29(6): 1408–1426) defined the concept of singly covered minimal elements. Let $L(n,\,k)$ denote the set of linked partitions of $[n]$ with $k$ singly covered minimal elements and let $P(n,\,k)$ denote the set of permutations of $[n]$ with $k$ cycles. In this paper, we mainly establish two bijections between $L(n,\,k)$ and $P(n,\,k)$. The two bijections from a different perspective show the one-to-one correspondence between the singly covered minimal elements in $L(n,\,k)$&nbsp;and the cycles in $P(n,\,k)$.&nbsp;</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2019.01.08},
url = {https://global-sci.com/article/81551/singly-covered-minimal-elements-of-linked-partitions-and-cycles-of-permutations}
}