On pseudo-Boolean polynomials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1952-1958
Cet article a éte moissonné depuis la source Math-Net.Ru
A pseudo-Boolean function is an arbitrary mapping of the set of binary $n$-tuples to the real line. Such functions are a natural generalization of classical Boolean functions and find numerous applications in various applied studies. Specifically, the Fourier transform of a Boolean function is a pseudo-Boolean function. A number of facts associated with pseudo-Boolean polynomials are presented, and their applications to well-known discrete optimization problems are described.
@article{ZVMMF_2015_55_11_a12,
author = {V. K. Leont'ev},
title = {On {pseudo-Boolean} polynomials},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1952--1958},
year = {2015},
volume = {55},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a12/}
}
V. K. Leont'ev. On pseudo-Boolean polynomials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 11, pp. 1952-1958. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_11_a12/
[1] Beresnev V. L., Diskretnye zadachi razmescheniya i polinomy ot bulevykh peremennykh, In-t Matem. SO RAN, Novosibirsk, 2005, 408 pp.
[2] Hammer P., Rudeanu S., “Pseudo-Boolean programming”, Operat. Res., 17:2 (1969), 233–261 | DOI | MR | Zbl
[3] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1980, 440 pp. | MR
[4] Zenkin A. I., Leontev V. K., “Ob odnoi neklassicheskoi zadache raspoznavaniya”, Zh. vychisl. matem. i matem. fiz., 24:6 (1984), 925–931 | MR | Zbl
[5] Leontev V. K., “Odna teorema o monotonnykh funktsiyakh”, Diskretnyi analiz, 1974, no. 6, 61–64