Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The M\"obius Function of Generalized Factor Order   We use discrete Morse theory to determine the M\"obius function of
generalized factor order. Ordinary factor order on the Kleene closure A* of a
set A is the partial order defined by letting u\leq w if w contains u as a
subsequence of consecutive letters. The M\"obius function of ordinary factor
order was determined by Bj\"orner. Using Babson and Hersh's application of
Robin Forman's discrete Morse theory to lexicographically ordered chains, we
are able to gain new understanding of Bj\"orner's result and its proof. We
generalize the notion of factor order to take into account a partial order on
the alphabet A and, relying heavily on discrete Morse theory, give a recursive
formula in the case where each letter of the alphabet covers a unique letter.

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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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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: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc