124 research outputs found
On a property of 2-dimensional integral Euclidean lattices
Let be any integral lattice in the 2-dimensional Euclidean space.
Generalizing the earlier works of Hiroshi Maehara and others, we prove that for
every integer , there is a circle in the plane that
passes through exactly points of .Comment: 9 page
On relative -designs in polynomial association schemes
Motivated by the similarities between the theory of spherical -designs and
that of -designs in -polynomial association schemes, we study two
versions of relative -designs, the counterparts of Euclidean -designs for
- and/or -polynomial association schemes. We develop the theory based on
the Terwilliger algebra, which is a noncommutative associative semisimple
-algebra associated with each vertex of an association scheme. We
compute explicitly the Fisher type lower bounds on the sizes of relative
-designs, assuming that certain irreducible modules behave nicely. The two
versions of relative -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.Comment: 17 page
On primitive symmetric association schemes with m_1=3
We classify primitive symmetric association schemes with
m_1 = 3. Namely, it is shown that the tetrahedron, i.e., the association scheme of the complete graph K_4, is the unique such association scheme. Our proof of this result is based on the spherical embeddings of association schemes and elementary three dimensional Euclidean geometry
On primitive symmetric association schemes with m_1=3
We classify primitive symmetric association schemes with
m_1 = 3. Namely, it is shown that the tetrahedron, i.e., the association scheme of the complete graph K_4, is the unique such association scheme. Our proof of this result is based on the spherical embeddings of association schemes and elementary three dimensional Euclidean geometry
On primitive symmetric association schemes with m_1=3
We classify primitive symmetric association schemes with
m_1 = 3. Namely, it is shown that the tetrahedron, i.e., the association scheme of the complete graph K_4, is the unique such association scheme. Our proof of this result is based on the spherical embeddings of association schemes and elementary three dimensional Euclidean geometry
On primitive symmetric association schemes with m_1=3
We classify primitive symmetric association schemes with
m_1 = 3. Namely, it is shown that the tetrahedron, i.e., the association scheme of the complete graph K_4, is the unique such association scheme. Our proof of this result is based on the spherical embeddings of association schemes and elementary three dimensional Euclidean geometry
- …