Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shape-Wilf-equivalences for vincular patterns   We extend the notion of shape-Wilf-equivalence to vincular patterns (also
known as "generalized patterns" or "dashed patterns"). First we introduce a
stronger equivalence on patterns which we call filling-shape-Wilf-equivalence.
When vincular patterns $\alpha$ and $\beta$ are filling-shape-Wilf-equivalent,
we prove that the direct sum $\alpha\oplus\sigma$ is
filling-shape-Wilf-equivalent to $\beta\oplus\sigma$. We also discover two new
pairs of patterns which are filling-shape-Wilf-equivalent: when $\alpha$,
$\beta$, and $\sigma$ are nonempty consecutive patterns which are
Wilf-equivalent, $\alpha\oplus\sigma$ is filling-shape-Wilf-equivalent to
$\beta\oplus\sigma$; and for any consecutive pattern $\alpha$, $1\oplus\alpha$
is filling-shape-Wilf-equivalent to $1\ominus\alpha$. These equivalences
generalize Wilf-equivalences found by Elizalde and Kitaev. These new
equivalences imply many new Wilf-equivalences for vincular patterns

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat