arXiv subjects
Publications and source records attributed to Jonathan I. Hall.
We calculate the spectrum of the diagram for each finite $3$-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras.
In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between $3$-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type $η$ admit a Frobenius form, for any $η$.
It has been noticed that all the known binary sequences having the asymptotic merit factor $\ge 6$ are the modifications to the real primitive characters. In this paper, we give a new modification of the character sequences at length $N=p_1p_2\dots p_r$, where $p_i$'s are distinct odd primes and $r$ is finite. Based on these new modifications, for $N=p_1p_2\dots p_r$ with $p_i$'s distinct odd primes, we can construct a binary sequence of length $2N$ with asymptotic merit factor $6.0$
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions { a, a+d, a+2d,...}.
In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.
We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups $O_{m}^{\pm}(3)$ with $m\geq6$ on nonsingular points of their standard modules. These actions together with those studied in \cite{HN} are all examples of primitive rank 3 actions of finite classical groups on nonsingular points.
We study the odd-characteristic structure of permutation modules for the rank 3 natural actions of $O_{2n}^{\pm}(2)$ ($n\geq3$) and $U_{m}(2)$ ($m\geq4$) on nonsingular points of their standard modules.
Based on the third author's thesis in this article we complete the local recognition of commuting reflection graphs of spherical Coxeter groups arising from irreducible crystallographic root systems.