Samuel Bevins | Searcharxiv

arXiv2026

Symmetry-guided constructions of absolutely maximally entangled states in five open cases

We give explicit Hermitian self-dual maximum distance separable codes with parameters $[12,6,7]_{25}$, $[18,9,10]_{121}$, and $[18,9,10]_{169}$. The stabilizer construction proves the existence of ${\rm AME}(12,5)$, ${\rm AME}(18,11)$, and ${\rm AME}(18,13)$ states; one-party projection also gives ${\rm AME}(17,11)$ and ${\rm AME}(17,13)$. The first code was found by a direct search. A regular $\mathbb{Z}_3^2$ coordinate orbit of its automorphism group suggested a group-circulant form that reduces each length-eighteen construction to a nine-entry kernel. The printed matrices are certified by exact Hermitian products and complete square-minor enumeration.

quant-ph↗

arXiv2022

2-step Nilpotent $L_\infty$-algebras and Hypergraphs

We describe a procedure to attach a nilpotent strong homotopy Lie algebra to every simple hypergraph and prove that two hypergraphs are isomorphic if and only if the corresponding strong homotopy Lie algebras are isomorphic. As an application, we characterize hypergraphs admitting a system of distinct representatives in terms of symplectic forms on the corresponding strong homotopy Lie algebra. We conclude with a combinatorial description of the cohomology of these strong homotopy Lie algebras in low degree.

math.CO↗