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- W2950570245 abstract "In this paper, we present a reduction algorithm which transforms $m$-regular partitions of $[n]={1, 2, ..., n}$ to $(m-1)$-regular partitions of $[n-1]$. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions in terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers." @default.
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- W2950570245 date "2004-06-09" @default.
- W2950570245 modified "2023-09-27" @default.
- W2950570245 title "Reduction of $m$-Regular Noncrossing Partitions" @default.
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