Enumerative combinatorics
Ascents and descents in 01-fillings of moon polyominoes
European Journal of Combinatorics
Major index for 01-fillings of moon polyominoes
Journal of Combinatorial Theory Series A
Mixed Statistics on 01-Fillings of Moon Polyominoes
SIAM Journal on Discrete Mathematics
Front Representation of Set Partitions
SIAM Journal on Discrete Mathematics
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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 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.