English

Good sequencings for small Mendelsohn triple systems

Combinatorics 2019-09-17 v1

Abstract

A Mendelsohn triple system of order vv (or MTS(v)(v)) is a decomposition of the complete graph into directed 3-cyles. We denote the directed 3-cycle with edges (x,y)(x,y), (y,z)(y,z) and (z,x)(z,x) by (x,y,z)(x,y,z), (y,z,x)(y,z,x) or (z,x,y)(z,x,y). An \ell-good sequencing of a MTS(v)(v) is a permutation of the points of the design, say [x1    xv][x_1 \; \cdots \; x_v], such that, for every triple (x,y,z)(x,y,z) in the design, it is not the case that x=xix = x_i, y=xjy = x_j and z=xkz = x_k with i<j<ki < j < k and ki+1k-i+1 \leq \ell; or with j<k<ij < k < i and ij+1i-j+1 \leq \ell; or with k<i<jk < i < j and jk+1j-k+1 \leq \ell.

Keywords

Cite

@article{arxiv.1909.06475,
  title  = {Good sequencings for small Mendelsohn triple systems},
  author = {Donald L. Kreher and Douglas R. Stinson and Shannon Veitch},
  journal= {arXiv preprint arXiv:1909.06475},
  year   = {2019}
}

Comments

121 pages

R2 v1 2026-06-23T11:15:03.909Z