Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Eigenvectors of the Zero Laplacian and Signless Laplacian
  Eigenvalues of a Uniform Hypergraph   In this paper, we show that the eigenvectors of the zero Laplacian and
signless Lapacian eigenvalues of a $k$-uniform hypergraph are closely related
to some configured components of that hypergraph. We show that the components
of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have
the same modulus. Moreover, under a {\em canonical} regularization, the phases
of the components of these eigenvectors only can take some uniformly
distributed values in $\{\{exp}(\frac{2j\pi}{k})\;|\;j\in [k]\}$. These
eigenvectors are divided into H-eigenvectors and N-eigenvectors. Eigenvectors
with minimal support is called {\em minimal}. The minimal canonical
H-eigenvectors characterize the even (odd)-bipartite connected components of
the hypergraph and vice versa, and the minimal canonical N-eigenvectors
characterize some multi-partite connected components of the hypergraph and vice
versa.

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The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys