arXiv subjects

Remi Salinas Schmeis

Publications and source records attributed to Remi Salinas Schmeis.

3 recordsLinked to original sources

arXiv2026

Vertex-transitive quantum graphs

We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial.

math.OA↗

arXiv2026

Structural properties of graphs and the Universal Difference Property

We study the Universal Difference Property (UDP) introduced by Altınok, Anders, Arreola, Asencio, Ireland, Sarıoğlan, and Smith, focusing on the relationship between the structural properties of a graph and UDP. We present condtions for when UDP must hold on unicyclic graphs. We then prove that if UDP does not hold on an edge-labeled graph, then it cannot hold on any subdivision of that graph. Additionally, we show that if an edge-labeled graph satisfies the pairwise edge-disjoint path property, then the graph satisfies UDP. Lastly, we explore the relationship between UDP and subgraphs and prove that trees and cycles are the only two families of connected graphs for which UDP must hold for any edge-labeling over any ring.

math.CO↗

arXiv2025

Remarks on orthogonality spaces

We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of $\mathbb{C}^3$ but not of that of $\mathbb{R}^3$. The second is a companion result to the result of Tau and Tserunyan \cite{Tau} that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice.

math-ph↗