Hilly poor noncrossing partitions and (2, 3)-Motzkin paths
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چکیده
A hilly poor noncrossing partition is a noncrossing partition with the properties : (1) each block has at most two elements, (2) in its linear representation, any isolated vertex is covered by some arc. This paper defines basic pairs as a combinatorial object and gives the number of hilly poor noncrossing partitions with n blocks, which is closely related to Maximal Davenport-Schinzel sequences. Authors introduce a class of generalized Motzkin paths called (i, j)-Motzkin paths, and present a bijection between hilly poor noncrossing partitions and (2, 3)-Motzkin paths. Specialization of the bijection deduces various results regarding 3-colored Motzkin paths, Catalan numbers, Motzkin numbers and Riordan numbers.
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تاریخ انتشار 2003