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### Common properties of table algebras and association schemes

A. Rahnamai Barghi
2008 Discrete Mathematics
This leads to the natural question which properties of association schemes stay valid for table algebras.  ...  In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too.  ...  Hirasaka and the other organizers committee of the Association Schemes, Codes and Designs which was held in the Pusan National University, for their hospitality and support.  ...

### Page 3308 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews
The concept of table algebra was originated in [Z. Arad and H. I. Blau, J. Algebra 138 (1991), no. 1, 137-185; MR 92f:20007] to study the common properties of the above three examples.  ...  Biinger, Standard integral table algebras with a faithful real element of degree 5 and width 3 (83-103); Mitsugu Hirasaka, The enumeration of primitive commutative association schemes (105-123).  ...

### Page 6057 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews
tables of association schemes.  ...  All the information of an association scheme can be derived from its table of characters.  ...

### On amorphic C-algebras [article]

Ilia Ponomarenko, A. Rahnamai Barghi
2006 arXiv   pre-print
An amorphic association scheme has the property that any of its fusion is also an association scheme.  ...  In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up to isomorphism by the multiset of its degrees and an additional  ...  It would be interesting to describe the properties of the group Aut(A) providing that the C-algebra A is homogeneous and amorphic. 4.3 We recall that a table algebra is a C-algebra with nonnegative structure  ...

### Algebraic generalization of Diffie–Hellman key exchange

Juha Partala
2018 Journal of Mathematical Cryptology
In addition, we present a brief survey on the algebraic properties of existing key exchange schemes and identify the source of commutativity and the family of underlying algebraic structures for each scheme  ...  Algebraically, these schemes need to provide some sort of commutativity to enable Alice and Bob to derive a common key on a public channel while keeping it computationally difficult for the adversary to  ...  We have gathered the essentially different key exchange schemes and their algebraic properties into Table 1 .  ...

### Applications of the Isolating Fusion Algorithm to Table Algebras and Association Schemes [article]

Allen Herman, Roghayeh Maleki
2022 arXiv   pre-print
groups; and (3) producing examples of non-Schurian fusions of Schurian association schemes whose adjacency matrices have noncyclotomic eigenvalues.  ...  We apply this algorithm to three problems: (1) computing the fusion lattices for small association schemes of a given order; (2) producing explicit realizations of association schemes with transitive automorphism  ...  Typical examples of based algebras are the group algebras of finite groups, adjacency algebras of finite association schemes or coherent configurations, table algebras, C-algebras, and reality-based algebras  ...

### On periodic approximate solutions of dynamical systems with a quadratic right-hand side [article]

Mikhail Malykh, Leonid Sevastianov
2021 arXiv   pre-print
The inheritance of periodicity and the Painlevé property by the approximate solution is investigated.  ...  Difference schemes are considered for dynamical systems ẋ = f (x) with a quadratic right-hand side, which have t-symmetry and are reversible.  ...  Introduction At the end of the last century, a study of the inheritance of algebraic properties of exact solutions of ordinary differential equations, including dynamical systems, by difference schemes  ...

### Page 2320 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews
Later on connections to other topics (like association schemes) were discovered. The dual of a table algebra is, in general, not a table algebra.  ...  Nilpotency property in table algebras. (English summary) J. Algebra 226 (2000), no. 2, 875-879. Table algebras were introduced in [Z. Arad and H. I. Blau, J.  ...

### Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

Takuya Ikuta, Akihiro Munemasa
2018 Special Matrices
First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and  ...  We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes.  ...  Acknowledgement: The work of A.M. was supported by JSPS KAKENHI grant number 17K05155. References  E. Bannai, Subschemes of some association schemes, J. Algebra 144 (1991), 167-188.  ...

### Computing Isomorphisms of Association Schemes and its Application

Izumi Miyamoto
2001 Journal of symbolic computation
We give an algorithm computing isomorphisms of association schemes using their algebraic property.  ...  Isomorphisms of association schemes are isomorphisms of edge-labeled regular graphs permitting to permute the labels.  ...  We improved our program to speed up the computation of isomorphisms by using the algebraic property of association schemes.  ...

### Monomials and polynomials: the long march towards a definition

Giorgio Bolondi, Federica Ferretti, Andrea Maffia
2018 Teaching Mathematics and its Applications
Features of these schemes are exemplified through the analysis of some algebra high school textbooks, looking at the proposed 'definitions' of monomials and polynomials.  ...  The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations.  ...  (IT1, p.3) 3 For Algebraic expression we found the widest variety of names and properties involved in the definition schemes.  ...

### A class of symmetric association schemes as inclusion of biplanes [article]

Ivica Martinjak
2014 arXiv   pre-print
We proved that B includes a partially balanced incomplete design with association scheme of three classes. Consequently, these structures are symmetric, having 2k-6 points.  ...  Let B be a nontrivial biplane of order k-2 represented by symmetric canonical incidence matrix with trace 1+ k2.  ...  Acknowledgement Author is thankful to Professor Dragutin Svrtan form the University of Zagreb for advices on this subject, especially related to Lemma 1.  ...

### Coherent configurations, association schemes and permutation groups [chapter]

Peter J. Cameron
2003 Groups, Combinatorics and Geometry
This paper gives a brief outline of the theory of coherent configurations and association schemes, and reports on some recent work on the connection between association schemes and permutation groups.  ...  The relationship between permutation groups and association schemes is quite subtle; there are groups which preserve no non-trivial association scheme, and other groups for which there is not a unique  ...  algebra of the association scheme.  ...

### Clifford theory for commutative association schemes

Akihide Hanaki
2008 Discrete Mathematics
In this paper, Clifford's well-known theorem on irreducible characters of finite groups is generalized to finite commutative association schemes.  ...  Our theorem relates irreducible characters of finite commutative schemes to those of their strongly normal closed subsets.  ...  Zieschang and anonymouse referees for many kind advices.  ...

### Page 6212 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews
They also possess many common features of association schemes.  ...  (RS-AOSUR-A; Ekaterinburg) A property of the character table for a finite group. (Russian.  ...
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