Generalized complete mappings, neofields, sequenceable groups and block designs. I

More R-sequenceable Groups

Sequenceable Groups and Related Topics

In 1980, about 20 years after sequenceable groups were introduced by Gordon to construct row-complete latin squares, Keedwell published a survey of all the available results concerning sequencings. This was updated (jointly with Dénes) in 1991 and a short overview, including results about complete mappings and Rsequencings, was given in the CRC Handbook of Combinatorial Designs in 1995. In Sect...

Laplacian eigenvalues and optimality: I. Block designs

Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups

We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v, 3, λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v, 3, λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if...

Non-Abelian Sequenceable Groups Involving ?-Covers

A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...