Tutte polynomials of q-cones

Abstract

We derive a formula for the Tutte polynomial t( G′; x, y) of a q-cone G′ of a GF( q)-representable geometry G in terms of t( G; x, y). We use this to construct collections of infinite sequences of GF( q)-representable geometries in which corresponding geometries are not isomorphic and yet have the same Tutte polynomial. We also use this to construct, for each positive integer k, sets of non-isomorphic GF( q)-representable geometries all of which have the same Tutte polynomial and vertical (or Whitney) connectivity at least k.