Block-avoiding sequencings of points in Steiner triple systems

Authors

Donald L. Kreher, Michigan Technological UniversityFollow
Douglas R. Stnson, University of Waterloo

Document Type

Article

Publication Date

6-2019

Department

Department of Mathematical Sciences

Abstract

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>3and 4-good sequencings exist for any STS(v) with v>71. 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.

Publisher's Statement

©The author(s). Article deposited here in compliance with publisher policies. Publisher's version of record: http://ajc.maths.uq.edu.au/pdf/74/ajc_v74_p498.pdf

Publication Title

The Australasian Journal of Combinatorics

Recommended Citation

Kreher, D. L., & Stnson, D. R. (2019). Block-avoiding sequencings of points in Steiner triple systems. The Australasian Journal of Combinatorics, 74(3).
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/481

Version

Publisher's PDF