Let $n>1$ be an integer and $p$ be a prime number. Denote by $\mathfrak{C}_{p^n}$ the class of non-thin association $p$-schemes of degree $p^n$. A sharp upper and lower bounds on the rank of schemes in $\mathfrak{C}_{p^n}$ with a certain order of thin radical are obtained. Moreover, all schemes in this class whose rank are equal to the lower bound are characterized and some schemes in this class whose rank are equal to the upper bound are constructed. Finally, it is shown that the scheme with minimum rank in $\mathfrak{C}_{p^n}$ is unique up to isomorphism, and it is a fusion of any association $p$-schemes with degree $p^n$.
@article{10_37236_3097,
author = {Fateme Raei Barandagh and Amir Rahnamai Barghi},
title = {On the rank of \(p\)-schemes},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {2},
doi = {10.37236/3097},
zbl = {1267.05295},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3097/}
}
TY - JOUR
AU - Fateme Raei Barandagh
AU - Amir Rahnamai Barghi
TI - On the rank of \(p\)-schemes
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3097/
DO - 10.37236/3097
ID - 10_37236_3097
ER -
%0 Journal Article
%A Fateme Raei Barandagh
%A Amir Rahnamai Barghi
%T On the rank of \(p\)-schemes
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3097/
%R 10.37236/3097
%F 10_37236_3097
Fateme Raei Barandagh; Amir Rahnamai Barghi. On the rank of \(p\)-schemes. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3097
