scholarly journals Characterization of the group association scheme of $A_{5}$ by its intersection numbers

1998 ◽  
Vol 50 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Masato TOMIYAMA
Keyword(s):  
Association Scheme ◽  
Intersection Numbers ◽  
Group Association

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

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takuya Ikuta ◽  
Akihiro Munemasa
Keyword(s):  
Association Scheme ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Association Schemes ◽  
Roots Of Unity ◽  
Galois Rings ◽  
Type Complex ◽  
Complex Hadamard Matrix

Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. 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 show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES

2018 ◽  
Vol 107 (1) ◽  
pp. 1-8 ◽  
Author(s):  
ANGELA AGUGLIA
Keyword(s):  
Projective Spaces ◽  
Intersection Numbers

We characterize Hermitian cones among the surfaces of degree$q+1$of$\text{PG}(3,q^{2})$by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of$\text{PG}(4,q^{2})$among quasi-Hermitian ones.

scholarly journals Molecular characterization of phytoplasma of 16SrI-B group association with Acalypha indica in India

3 Biotech ◽  
2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Ajay K. Tiwari ◽  
M. S. Khan ◽  
Pradeep Kumar ◽  
Akhilesh Tiwari
Keyword(s):  
Molecular Characterization ◽  
Group Association ◽  
Acalypha Indica

scholarly journals On Relative $t$-Designs in Polynomial Association Schemes

10.37236/4889 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Eiichi Bannai ◽  
Etsuko Bannai ◽  
Sho Suda ◽  
Hajime Tanaka
Keyword(s):  
Lower Bounds ◽  
Association Scheme ◽  
Point Of View ◽  
Association Schemes ◽  
Algebraic Characterization ◽  
Terwilliger Algebra ◽  
C Algebra ◽  
Irreducible Modules

Motivated by the similarities between the theory of spherical $t$-designs and that of $t$-designs in $Q$-polynomial association schemes, we study two versions of relative $t$-designs, the counterparts of Euclidean $t$-designs for $P$- and/or $Q$-polynomial association schemes. We develop the theory based on the Terwilliger algebra, which is a noncommutative associative semisimple $\mathbb{C}$-algebra associated with each vertex of an association scheme. We compute explicitly the Fisher type lower bounds on the sizes of relative $t$-designs, assuming that certain irreducible modules behave nicely. The two versions of relative $t$-designs turn out to be equivalent in the case of the Hamming schemes. From this point of view, we establish a new algebraic characterization of the Hamming schemes.

A characterization of quadrics by intersection numbers

2007 ◽  
Vol 47 (1-3) ◽  
pp. 165-175 ◽  
Author(s):  
Jeroen Schillewaert
Keyword(s):  
Intersection Numbers
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