Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-Quasi-Ordering of Matrices under Schur Complement and Applications
  to Directed Graphs   In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric
Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field
$\mathbf{F}$, any infinite sequence $M_1,M_2,...$ of (skew) symmetric matrices
over $\mathbf{F}$ of bounded $\mathbf{F}$-rank-width has a pair $i< j$, such
that $M_i$ is isomorphic to a principal submatrix of a principal pivot
transform of $M_j$. We generalise this result to $\sigma$-symmetric matrices
introduced by Rao and myself in [The Rank-Width of Edge-Coloured Graphs,
arXiv:0709.1433v4]. (Skew) symmetric matrices are special cases of
$\sigma$-symmetric matrices. As a by-product, we obtain that for every infinite
sequence $G_1,G_2,...$ of directed graphs of bounded rank-width there exist a
pair $i<j$ such that $G_i$ is a pivot-minor of $G_j$. Another consequence is
that non-singular principal submatrices of a $\sigma$-symmetric matrix form a
delta-matroid. We extend in this way the notion of representability of
delta-matroids by Bouchet.

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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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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: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom