Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A decomposition of ballot permutations, pattern avoidance and Gessel
  walks   A permutation whose any prefix has no more descents than ascents is called a
ballot permutation. In this paper, we present a decomposition of ballot
permutations that enables us to construct a bijection between ballot
permutations and odd order permutations, which proves a set-valued extension of
a conjecture due to Spiro using the statistic of peak values. This bijection
also preserves the neighbors of the largest letter in permutations and thus
resolves a refinement of Spiro' s conjecture proposed by Wang and Zhang. Our
decomposition can be extended to well-labelled positive paths, a class of
generalized ballot permutations arising from polytope theory, that were
enumerated by Bernardi, Duplantier and Nadeau. We will also investigate the
enumerative aspect of ballot permutations avoiding a single pattern of length 3
and establish a connection between 213-avoiding ballot permutations and Gessel
walks.

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The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga