Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Finiteness of the Twisted Bruhat Orders on Affine Weyl Groups   In this paper, we investigate various properties of strong and weak twisted
Bruhat orders on a Coxeter group. In particular, we prove that any twisted
strong Bruhat order on an affine Weyl group is locally finite, strengthening a
result of Dyer in J. Algebra, 163, 861--879 (1994). We also show that for a
non-finite and non-cofinite biclosed set $B$ in the positive system of an
affine root system with rank greater than 2, the set of elements having a fixed
$B$-twisted length is infinite. This implies that the twisted strong and weak
Bruhat orders have an infinite antichain in those cases. Finally, we show that
twisted weak Bruhat order can be applied to the study of the tope poset of an
infinite oriented matroid arising from an affine root system.

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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: adap-org