Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no l consecutive points in this permutation contain a block of the design. Such a permutation is called an l-good sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3 and 4-good sequencings exist for any STS(v) with v\u3e71. Similar re-sults also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v =7, 9, 13 and 15

Block-avoiding sequencings of points in Steiner triple systems

Given an STS(v), we ask if there is a permutation of the points of the design such that no L consecutive points in this permutation contain a block of the design. Such a permutation is called an L-good sequencing. We prove that 3-good sequencings exist for any STS(v) with v\u3e3and 4-good sequencings exist for any STS(v) with v\u3e71. Similar results also hold for partial STS(v). Finally, we determine the existence or nonexistence of 4-good sequencings for all the nonisomorphic STS(v) with v=7,9,13 and 15

On orthogonal generalized equitable rectangles

In this note, we give a complete solution of the existence of orthogonal generalized equitable rectangles, which was raised as an open problem in [4]. Key words: orthogonal latin squares, orthogonal equitable rectangles,

Constructions and bounds for codes with restricted overlaps

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which over-laps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein [9] in 1964

Constructions and bounds for codes with restricted overlaps

Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden. We prove some general bounds and we give several constructions in the case of binary codes. Our techniques also allow us to provide an alternative, elementary proof of a lower bound on non-overlapping codes due to Levenshtein in 1964.Comment: 25 pages. Extra citations, typos corrected and explanations expande

Bussey systems and Steiner\u27s tactical problem

In 1853, Steiner posed a number of combinatorial (tactical) problems, which eventually led to a large body of research on Steiner systems. However, solutions to Steiner\u27s questions coincide with Steiner systems only for strengths two and three. For larger strengths, essentially only one class of solutions to Steiner\u27s tactical problems is known, found by Bussey more than a century ago. In this paper, the relationships among Steiner systems, perfect binary one-error-correcting codes, and solutions to Steiner\u27s tactical problem (Bussey systems) are discussed. For the latter, computational results are provided for at most 15 points

Orthogonal Arrays of Strength Three from Regular 3-Wise Balanced Designs

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction

Ozone-depleting substances (ODSs) and related chemicals

The amended and adjusted Montreal Protocol continues to be successful at reducing emissions and atmospheric abundances of most controlled ozone-depleting substances (ODSs).Global Ozone Research and Monitoring Projec