Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The projective dimension of sequentially Cohen-Macaulay monomial ideals   In this short note we prove that the projective dimension of a sequentially
Cohen-Macaulay square-free monomial ideal is equal to the maximal height of its
minimal primes (also known as the big height), or equivalently, the maximal
cardinality of a minimal vertex cover of its facet complex. This in particular
gives a formula for the projective dimension of facet ideals of these classes
of ideals, which are known to be sequentially Cohen-Macaulay: graph trees and
simplicial trees, chordal graphs and some cycles, chordal clutters and graphs,
and some path ideals to mention a few. Since polarization preserves projective
dimension, our result also gives the projective dimension of any sequentially
Cohen-Macaulay monomial ideal.

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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga