It is well known that a rank-$r$ matroid $M$ is uniquely determined by its circuits of size at most $r$. This paper proves that if $M$ is binary and $r\ge 3$, then $M$ is uniquely determined by its circuits of size at most $r-1$ unless $M$ is a binary spike or a special restriction thereof. In the exceptional cases, $M$ is determined up to isomorphism.
@article{10_37236_5373,
author = {James Oxley and Charles Semple and Geoff Whittle},
title = {Determining a binary matroid from its small circuits},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {1},
doi = {10.37236/5373},
zbl = {1330.05033},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5373/}
}
TY - JOUR
AU - James Oxley
AU - Charles Semple
AU - Geoff Whittle
TI - Determining a binary matroid from its small circuits
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/5373/
DO - 10.37236/5373
ID - 10_37236_5373
ER -
%0 Journal Article
%A James Oxley
%A Charles Semple
%A Geoff Whittle
%T Determining a binary matroid from its small circuits
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5373/
%R 10.37236/5373
%F 10_37236_5373
James Oxley; Charles Semple; Geoff Whittle. Determining a binary matroid from its small circuits. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5373
