Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splittings of monomial ideals   We provide some new conditions under which the graded Betti numbers of a
monomial ideal can be computed in terms of the graded Betti numbers of smaller
ideals, thus complementing Eliahou and Kervaire's splitting approach. As
applications, we show that edge ideals of graphs are splittable, and we provide
an iterative method for computing the Betti numbers of the cover ideals of
Cohen-Macaulay bipartite graphs. Finally, we consider the frequency with which
one can find particular splittings of monomial ideals and raise questions about
ideals whose resolutions are characteristic-dependent.

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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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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: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: cs