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- W2036719217 abstract "In this paper we present a new combinatorial class enumerated by Catalan numbers. More precisely, we establish a bijection between the set of partitions π 1 π 2 ⋯ π n of [ n ] such that π i + 1 − π i ≤ 1 for all i = , 1 , 2 … , n − 1 , and the set of Dyck paths of semilength n . Moreover, we find an explicit formula for the generating function for the number of partitions π 1 π 2 ⋯ π n of [ n ] such that either π i + ℓ − π i ≤ 1 for all i = 1 , 2 , … , n − ℓ , or π i + 1 − π i ≤ m for all i = 1 , 2 , … , n − 1 ." @default.
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- W2036719217 date "2009-07-01" @default.
- W2036719217 modified "2023-09-28" @default.
- W2036719217 title "Partitions of a set satisfying certain set of conditions" @default.
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- W2036719217 doi "https://doi.org/10.1016/j.disc.2009.02.010" @default.
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