A characterisation of jointless Dowling geometries Original Research Article

We use statistics of flats of small rank in order to characterise the jointless Dowling geometries defined by groups of order exceeding three and having rank greater than 3. In particular, we show that if the Tutte polynomial of a matroid is identical to the Tutte polynomial of a jointless Dowling geometry, then the matroid is indeed a jointless Dowling geometry. For rank 3 (and groups of order exceeding 3) this holds only if the order of the group is even.