Block-avoiding sequencings of points in Steiner triple systems

Authors

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

Document Type

Article

Publication Date

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 sequenc-ing. We prove that 3-good sequencings exist for any STS(v) with v>3 and 4-good sequencings exist for any STS(v) with v>71. 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.

Publisher's Statement

© The author(s). Released under the CC BY-ND 4.0 International License. Publisher’s version of record: http://ajc.maths.uq.edu.au/pdf/74/ajc_v74_p498.pdf

Publication Title

AUSTRALASIAN JOURNAL OF COMBINATORICS

Recommended Citation

Kreher, D. L., & Stinson, D. R. (2019). Block-avoiding sequencings of points in Steiner triple systems. AUSTRALASIAN JOURNAL OF COMBINATORICS, 74(3), 498-509.
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/600

Creative Commons License

This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 International License.

Version

Publisher's PDF