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- W2025218149 abstract "We give a simple and natural proof of (an extension of) the identity P ( k , l , n ) = P 2 ( k − 1, l − 1, n − 1). The number P ( k , l , n ) counts noncrossing partitions of {1, 2, …, l } into n parts such that no part contains two numbers x and y , 0 < y − x < k . The lower index 2 indicates partitions with no part of size three or more. We use the identity to give quick proofs of the closed formulae for P ( k , l , n ) when k is 1, 2, or 3." @default.
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- W2025218149 date "1998-03-01" @default.
- W2025218149 modified "2023-09-26" @default.
- W2025218149 title "On trees and noncrossing partitions" @default.
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- W2025218149 doi "https://doi.org/10.1016/s0166-218x(97)00118-2" @default.
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