Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Genericity of Filling Elements   An element of a finitely generated non-Abelian free group F(X) is said to be
filling if that element has positive translation length in every very small
action of F(X) on an $\mathbb{R}$-tree. We give a proof that the set of filling
elements of F(X) is exponentially F(X)-generic in the sense of Arzhantseva and
Ol'shanskii. We also provide an algebraic sufficient condition for an element
to be filling and show that there exists an exponentially F(X)-generic subset
of filling elements whose membership problem is solvable in linear time.

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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con