# Bibliography

Research Report

### Basic facts concerning extreme supermodular functions

**: **ÚTIA AV ČR v.v.i,
(Praha 2016)

**: **Research Report 2359

**: **GA16-12010S, GA ČR

**: **supermodular function,
standardizations,
extreme supermodular function

**: **http://library.utia.cas.cz/separaty/2016/MTR/studeny-0467581.pdf

**(eng): **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\nand 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.

**: **BA