Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Categorification of the Vandermonde Determinant   In the spirit of Bar Natan's construction of Khovanov homology, we give a
categorification of the Vandermonde determinant. Given a sequence of positive
integers $\vec{x}=(x_1,...,x_n)$, we construct a commutative diagram in the
shape of the Bruhat order on $S_n$ whose nodes are colored smoothings of the
$2$-strand torus link $T_{2,n}$, and whose arrows are colored cobordisms. An
application of a TQFT to this diagram yields a chain complex whose Euler
characteristic is the Vandermonde determinant evaluated at $\vec{x}$. A
generalization to arbitrary link diagrams is given, producing categorifications
of certain generalized Vandermonde determinants. We also address functoriality
of this construction.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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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: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg