Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak ascent sequences and related combinatorial structures   In this paper we introduce {\em weak ascent sequences}, a class of number
sequences that properly contains ascent sequences. We show how these sequences
uniquely encode each of the following objects: permutations avoiding a
particular length-4 bivincular pattern; upper-triangular binary matrices that
satisfy a column-adjacency rule; factorial posets that contain no {\em weak}
(3+1) subposet. We also show how weak ascent sequences are related to a class
of pattern avoiding inversion sequences that has been a topic of recent
research by Auli and Elizalde. Finally, we consider the problem of enumerating
these new sequences and give a closed form expression for the number of weak
ascent sequences having a prescribed length and number of weak ascents.

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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph