Contiguous orthogonal systems

Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1 Mendelsohn Triple Systems excluding Contiguous Units with Λ = 1

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with λ = 1. Also, we obtain the spectrum for cyclic such systems.

Orthogonal relational systems

Subspaces and orthogonal decompositions generated by bounded orthogonal systems

We investigate properties of subspaces of L2 spanned by subsets of a finite orthonormal system bounded in the L∞ norm. We first prove that there exists an arbitrarily large subset of this orthonormal system on which the L1 and the L2 norms are close, up to a logarithmic factor. Considering for example the Walsh system, we deduce the existence of two orthogonal subspaces of L2 , complementary to...

Orthogonal systems in finite graphs

Let Γ be a finite graph and GΓ be the corresponding free partially commutative group. In this paper we construct orthogonality theory for graphs and free partially commutative groups. The theory developed here provides tools for the study of the structure of the centraliser lattice of partially commutative groups.

Orthogonal resolutions of triple systems

Existence results concerning double and multiple orthogonal resolutions of triple are and a number of open nlll~~tl0Tl!'l mentioned.