Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite Thurston type orderings of braid groups   We prove that for any finite Thurston-type ordering $<_{T}$ on the braid
group\ $B_{n}$, the restriction to the positive braid monoid
$(B_{n}^{+},<_{T})$ is a\ well-ordered set of order type
$\omega^{\omega^{n-2}}$. The proof uses a combi\ natorial description of the
ordering $<_{T}$. Our combinatorial description is \ based on a new normal form
for positive braids which we call the $\C$-normal fo\ rm. It can be seen as a
generalization of Burckel's normal form and Dehornoy's \ $\Phi$-normal form
(alternating normal form).

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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn