This paper provides a model of the use of computer algebra experimentation in algebraic graph theory. Starting from the semisymmetric cubic graph L on 112 vertices, we embed it into another semisymmetric graph N of valency 15 on the same vertex set. In order to consider systematically the links between L and N a number of combinatorial structures are involved and related coherent configurations...

The semisymmetrization of an arbitrary quasigroup builds a semisymmetric structure on the cube underlying set quasigroup. It serves to reduce homotopies homomorphisms. An alternative square was recently introduced by A. Krapež and Z. Petrić. Their construction in fact yields Mendelsohn quasigroup, which is idempotent as well semisymmetric. We describe it Mendelsohnization original For quasigrou...

It is proved that any non-normable Fréchet space with a semisymmetric absolute basis is isomorphic to the space ω of all scalar sequences. A similar result is shown for quasi-homogeneous absolute bases. It is also proved that any nuclear Fréchet space with a semi-subsymmetric basis is isomorphic to ω.

In this paper we investigate a new family of multivariable polynomials. These polynomials, denoted Rλ(z1, . . . , zn; r), depend on a parameter r and are indexed by a partition λ of length n. Up to a scalar, Rλ is characterized by the following elementary properties: • Rλ is symmetric in the odd variables z1, z3, z5, . . . as well as in the even variables z2, z4, z6, . . .. Polynomials having t...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...