Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerative combinatorics on determinants and signed bigrassmannian
  polynomials   As an application of linear algebra for enumerative combinatorics, we
introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian
determinant. First, a signed bigrassmannian polynomial is a variant of the
statistic given by the number of bigrassmannian permutations below a
permutation in Bruhat order as Reading suggested (2002) and afterward the
author developed (2011). Second, bigrassmannian determinant is a $q$-analog of
the determinant with respect to our statistic. It plays a key role for a
determinantal expression of those polynomials. We further show that
bigrassmannian determinant satisfies weighted condensation as a generalization
of Dodgson, Jacobi-Desnanot and Robbins-Rumsey (1986).

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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int