Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Basic facts concerning supermodular functions   Elementary facts and observations on the cone of supermodular set functions
are recalled. The manuscript deals with such operations with set functions
which preserve supermodularity and the emphasis is put on those such operations
which even preserve extremality (of a supermodular function). These involve a
few self-transformations of the cone of supermodular set functions. Moreover,
projections to the (less-dimensional) linear space of set functions for a
subset of the variable set are discussed. Finally, several extensions to the
(more-dimensional) linear space of set functions for a superset of the variable
set are shown to be both preserving supermodularity and extremality.

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The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom