Geodesic
On a conjecture concerning dyadic oriented matroids
The electronic journal of combinatorics, Tome 6 (1999)
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A rational matrix is totally dyadic if all of its nonzero subdeterminants are in $\{\pm 2^k\ :\ k \in {\bf Z}\}$. An oriented matriod is dyadic if it has a totally dyadic representation $A$. A dyadic oriented matriod is dyadic of order $k$ if it has a totally dyadic representation $A$ with full row rank and with the property that for each pair of adjacent bases $A_1$ and $A_2$ $$2^{-k} \le \left| { {\det(A_1)} \over {\det(A_2)}}\right|\le 2^k.$$ In this note we present a counterexample to a conjecture on the relationship between the order of a dyadic oriented matroid and the ratio of agreement to disagreement in sign of its signed circuits and cocircuits (Conjecture 5.2, Lee (1990)).
DOI : 10.37236/1455
Classification : 05B35
Mots-clés : dyadic oriented matroid, signed circuits, cocircuits 
@article{10_37236_1455,
     author = {Matt Scobee},
     title = {On a conjecture concerning dyadic oriented matroids},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1455},
     zbl = {0918.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1455/}
}
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Matt Scobee. On a conjecture concerning dyadic oriented matroids. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1455

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