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- W2950642020 abstract "Babson and Steingr'{i}msson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider n-permutations that avoid the generalized pattern 1-32 and whose k rightmost letters form an increasing subword. The number of such permutations is a linear combination of Bell numbers. We find a bijection between these permutations and all partitions of an $(n-1)$-element set with one subset marked that satisfy certain additional conditions. Also we find the e.g.f. for the number of permutations that avoid a generalized 3-pattern with no dashes and whose k leftmost or k rightmost letters form either an increasing or decreasing subword. Moreover, we find a bijection between n-permutations that avoid the pattern 132 and begin with the pattern 12 and increasing rooted trimmed trees with n+1 nodes." @default.
- W2950642020 created "2019-06-27" @default.
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- W2950642020 date "2002-05-20" @default.
- W2950642020 modified "2023-09-23" @default.
- W2950642020 title "Generalized pattern avoidance with additional restrictions" @default.
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