Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension filtration, sequential Cohen--Macaulayness and a new
  polynomial invariant of graded algebras   Let $\k$ be a field and let $A$ be a standard $\mathbb{N}$-graded
$\k$-algebra. Using numerical information of some invariants in the primary
decomposition of $0$ in $A$, namely the so called dimension filtration, we
associate a bivariate polynomial $\BW(A;t,w)$, that we call the
Bj\"{o}rner--Wachs polynomial, to $A$.
  It is shown that the Bj\"{o}rner--Wachs polynomial is an algebraic
counterpart of the combinatorially defined $h$-triangle of finite simplicial
complexes introduced by Bj\"{o}rner \& Wachs. We provide a characterisation of
sequentially Cohen--Macaulay algebras in terms of the effect of the reverse
lexicographic generic initial ideal on the Bj\"{o}rner--Wachs polynomial. More
precisely, we show that a graded algebra is sequentially Cohen--Macaulay if and
only if it has a stable Bj\"{o}rner--Wachs polynomial under passing to the
reverse lexicographic generic initial ideal. We conclude by discussing
connections with the Hilbert series of local cohomology modules.

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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom