arXiv subjects

Imane Souktani

Publications and source records attributed to Imane Souktani.

2 recordsLinked to original sources

arXiv2021

$k$-spectrally monomorphic tournaments

A tournament is $k$-spectrally monomorphic if all the $k\times k$ principal submatrices of its adjacency matrix have the same characteristic polynomial. Transitive $n$-tournaments are trivially $k$-spectrally monomorphic. We show that there are no other for $k\in \{3,\ldots,n-3\} $. Furthermore, we prove that for $n\geq 5$, a non-transitive $n$-tournament is $(n-2)$-spectrally monomorphic if and only if it is doubly regular. Finally, we give some results on $(n-1)$-spectrally monomorphic regular tournaments.

math.CO↗

arXiv2021

Characterization of $k$-spectrally monomorphic Hermitian matrices

This paper solves the following problem about Hermitian matrices related to the theory of $2$-structures:\emph{ }Let $n$ be a positive integer and $k$ be an integer with $k\in \{3,\ldots,n-3\}$. Characterize the Hermitian matrices $A$ such that the characteristic polynomials of the $k\times k$ submatrices of $A$ are all equal. Such matrices are called $k$-spectrally monomorphic. A crucial step to obtain this characterization is proving that if a matrix $A$ is $k$-spectrally monomorphic then it is $l$-spectrally monomorphic for $l$ in $\{1,\ldots,min\{k, n-k\}\}$.

math.CO↗