On the Rank of $p$-Schemes
| Autor: | Amir Rahnamai Barghi, Fateme Raei Barandagh |
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| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
Degree (graph theory) Applied Mathematics Prime number Order (ring theory) Upper and lower bounds Theoretical Computer Science Combinatorics Association scheme Computational Theory and Mathematics Integer Discrete Mathematics and Combinatorics Rank (graph theory) Geometry and Topology Isomorphism Mathematics |
| Zdroj: | The Electronic Journal of Combinatorics. 20 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/3097 |
| Popis: | 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 $p^n$. |
| Databáze: | OpenAIRE |
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