Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Weak Lefschetz Property for Hilbert functions of almost complete
  intersections   It is known that all complete intersection Artinian standard graded algebras
of codimension 3 have the Weak Lefschetz Property. Unfortunately, this property
does not continue to be true when you increase the number of minimal generators
for the ideal defining the algebra. For instance, it is not more valid for
almost complete intersection Artinian standard graded algebras of codimension
3. On the other hand, the Hilbert functions of all Weak Lefschetz Artinian
graded algebras are unimodal and with the positive part of their first
difference forming an $O$-sequence (i.e. are Weak Lefschetz sequences). In this
paper we show that all the Hilbert functions of the almost complete
intersection Artinian standard graded algebras of codimension 3 are Weak
Lefschetz sequences.

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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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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: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc