Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted associativity of the cyclically reduced product of words, part 2   The cyclically reduced product of two words $u, v$, denoted $u * v$, is the
cyclically reduced form of the concatenation of $u$ by $v$. This product is not
associative. Recently S. V. Ivanov has proved that the Andrews-Curtis
conjecture can be restated in terms of the cyclically reduced product and
cyclic permutations instead of the reduced product and conjugations.
  In a previous paper we have proved that $*$ verifies generalizations of
properties of the product in the free group. In another previous paper we have
proved that $*$ verifies a generalized version of the associativity property in
a special case. In the present paper we prove that a more general version of
the associativity property holds for $*$ in the general case.

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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph