Geodesic
On the $id$-decompositions of the class~$P_k$ over precomplete classes
Diskretnaya Matematika, Tome 5 (1993) no. 2, pp. 98-110

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a representation of functions $f(x_1,\cdots,x_n)$ in $P_k$ in the form $$ g(x_1,\dots,x_m,F^1_2,\dots,F^1_m,\dots,F^m_1,\dots,F^m_{m-1}), $$ where $2\le m\le n$ and $F^i_j=f(x_1,\dots,x_{j-1},x_i,x_{j+1},\dots,x_n)$ for $i\ne j$. We investigate the possibility of such representations with $g$ belonging to classes that are precomplete in $P_k$. We give upper bounds on the parameter $m$ in the representation. 
@article{DM_1993_5_2_a7,
     author = {S. S. Marchenkov},
     title = {On the $id$-decompositions of the class~$P_k$ over precomplete classes},
     journal = {Diskretnaya Matematika},
     pages = {98--110},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1993_5_2_a7/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - On the $id$-decompositions of the class~$P_k$ over precomplete classes
JO  - Diskretnaya Matematika
PY  - 1993
SP  - 98
EP  - 110
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_1993_5_2_a7/
LA  - ru
ID  - DM_1993_5_2_a7
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T On the $id$-decompositions of the class~$P_k$ over precomplete classes
%J Diskretnaya Matematika
%D 1993
%P 98-110
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_1993_5_2_a7/
%G ru
%F DM_1993_5_2_a7
S. S. Marchenkov. On the $id$-decompositions of the class~$P_k$ over precomplete classes. Diskretnaya Matematika, Tome 5 (1993) no. 2, pp. 98-110. http://geodesic.mathdoc.fr/item/DM_1993_5_2_a7/