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pro vyhledávání: '"Herman, Allen A."'
Terwilliger algebras are finite-dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance-regular graphs. The Terwilliger algebras of the conjugacy class association schemes
Externí odkaz:
http://arxiv.org/abs/2411.08803
We study the minimum number of distinct eigenvalues over a collection of matrices associated with a graph. Lower bounds are derived based on the existence or non-existence of certain cycle(s) in a graph. A key result proves that every Johnson graph h
Externí odkaz:
http://arxiv.org/abs/2411.00250
Given a prime number $p$, we consider the tower of finite fields $F_p=L_{-1}\subset L_0\subset L_1\subset\cdots$, where each step corresponds to an Artin-Schreier extension of degree $p$, so that for $i\geq 0$, $L_{i}=L_{i-1}[c_{i}]$, where $c_i$ is
Externí odkaz:
http://arxiv.org/abs/2405.10159
Autor:
Herman, Allen
The Terwilliger algebras of asymmetric association schemes of rank $3$, whose nonidentity relations correspond to doubly regular tournaments, are shown to have thin irreducible modules, and to always be of dimension $4k+9$ for some positive integer $
Externí odkaz:
http://arxiv.org/abs/2404.11560
Autor:
Herman, Allen, Maleki, Roghayeh
Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection of non-negative integer parameters of size $d + \f
Externí odkaz:
http://arxiv.org/abs/2309.03657
Autor:
Herman, Allen, Joshi, Neha
In this paper we determine all fusions of the association scheme $\mathcal{A} \otimes \mathcal{A}$, where $\mathcal{A}$ is the symmetric rank $3$ association scheme corresponding to a strongly regular graph. This includes both guaranteed fusions, whi
Externí odkaz:
http://arxiv.org/abs/2306.00878
Autor:
Babei, Angelica, Herman, Allen
We calculate zeta functions for certain orders of rank $3$ defined by standard integral table algebras and integral fusion rings that have irrational-valued irreducible characters. The calculations are obtained from explicit calculations of zeta inte
Externí odkaz:
http://arxiv.org/abs/2304.13602
Autor:
Herman, Allen, Maleki, Roghayeh
Let $\mathbf{B}$ be a basis for an $r$-dimensional algebra $A$ over a field or commutative ring with unity. The semifusions of $\mathbf{B}$ are the partitions of $\mathbf{B}$ whose characteristic functions form the basis of a subalgebra of $A$, and f
Externí odkaz:
http://arxiv.org/abs/2205.01810
Autor:
Babei, Angelica, Herman, Allen
We investigate Solomon's zeta function for orders in the special case of orders generated by the standard basis of an integral table algebra, a special case of which is the integral adjacency algebra of an association scheme. As Solomon's elementary
Externí odkaz:
http://arxiv.org/abs/2204.04784
As a main result of this paper we give conditions under which the generalized $X$-join of Cayley graphs is a Cayley graph. In particular, we show that $X$-join of isomorphic Cayley graphs is a Cayley grpah. To do this, new properties for a generalize
Externí odkaz:
http://arxiv.org/abs/2203.07819