Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized pattern avoidance with additional restrictions   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.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph