Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally monotone Boolean and pseudo-Boolean functions   We propose local versions of monotonicity for Boolean and pseudo-Boolean
functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone
if none of its partial derivatives changes in sign on tuples which differ in
less than p positions. As it turns out, this parameterized notion provides a
hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local
monotonicities are shown to be tightly related to lattice counterparts of
classical partial derivatives via the notion of permutable derivatives. More
precisely, p-locally monotone functions are shown to have p-permutable lattice
derivatives and, in the case of symmetric functions, these two notions
coincide. We provide further results relating these two notions, and present a
classification of p-locally monotone functions, as well as of functions having
p-permutable derivatives, in terms of certain forbidden "sections", i.e.,
functions which can be obtained by substituting constants for variables. This
description is made explicit in the special case when p=2.

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The categories of this paper are: comp-gas
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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: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an