Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Avoiding a pair of patterns in multisets and compositions   In this paper, we study the Wilf-type equivalence relations among multiset
permutations. We identify all multiset equivalences among pairs of patterns
consisting of a pattern of length three and another pattern of length at most
four. To establish our results, we make use of a variety of techniques,
including Ferrers-equivalence arguments, sorting by minimal/maximal letters,
analysis of active sites and direct bijections. In several cases, our arguments
may be extended to prove multiset equivalences for infinite families of pattern
pairs. Our results apply equally well to the Wilf-type classification of
compositions, and as a consequence, we obtain a complete description of the
Wilf-equivalence classes for pairs of patterns of type (3,3) and (3,4) on
compositions, with the possible exception of two classes of type (3,4).

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The categories of this paper are: q-alg
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th