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- W2040306972 abstract "A partition u of [ k ] = {1, 2,⋯ , k } is contained in another partition v of [ l ] if [ l ] has a k -subset on which v induces u . We are interested in counting partitions v not containing a given partition u or a given set of partitions R . This concept is related to that of forbidden permutations. A strengthening of the Stanley–Wilf conjecture is proposed. We prove that the generating function (GF) counting v is rational if (i) R is finite and the number of parts of v is fixed or if (ii) u has only singleton parts and at most one doubleton part. In fact, (ii) is an application of (i). As another application of (i) we prove that for each k the GF counting partitions with k pairs of crossing parts belongs to Z (1 − 4 x )." @default.
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- W2040306972 date "2000-03-01" @default.
- W2040306972 modified "2023-09-26" @default.
- W2040306972 title "Counting Pattern-free Set Partitions I: A Generalization of Stirling Numbers of the Second Kind" @default.
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- W2040306972 doi "https://doi.org/10.1006/eujc.1999.0353" @default.
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