Grant: Discovery Grants Program - Individual

Skolem-Langford type sequences are generalizations of Skolem sequences. ASkolem sequence is a sequence of pairs of numbers from 1 to n, such that the 1s are one position apart, the 2s are 2 positions apart, etc. For example, 3,5,2,3,2,4,5,1,1,4 is a Skolem sequence of order n=5. This concept which was discovered by Skolem is closely related to important mathematical concepts such as the golden ratio, Steiner triple systems and difference number sets. Skolem-Langford type sequences also help as research tools that serve several branches in combinatorics, cyclic designs, mandatory representation designs and graph factorizations. Recently, applications of Skolem-Langford sequences were used to construct statistical experiments and optical orthogonal codes. We intend to work on proving several open conjectures concerning in these sequences (near-extended Skolem...) and several applications of these sequences. We also planning to generalize results in packing and covering designs. These generalizations are important to statistical designs of experiments and the creation of perfect insertion/deletion error correcting codes which, in turn, important for the development of methods to recover DNA sequences from error.