Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Fenchel Duality for a Pair of Integrally Convex and Separable
  Convex Functions   Discrete Fenchel duality is one of the central issues in discrete convex
analysis. The Fenchel-type min-max theorem for a pair of integer-valued
M-natural-convex functions generalizes the min-max formulas for polymatroid
intersection and valuated matroid intersection. In this paper we establish a
Fenchel-type min-max formula for a pair of integer-valued integrally convex and
separable convex functions. Integrally convex functions constitute a
fundamental function class in discrete convex analysis, including both
M-natural-convex functions and L-natural-convex functions, whereas separable
convex functions are characterized as those functions which are both
M-natural-convex and L-natural-convex. The theorem is proved by revealing a
kind of box integrality of subgradients of an integer-valued integrally convex
function. The proof is based on the Fourier-Motzkin elimination.

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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph