Gaussian, Strong and Transversal Greedoids

Various types of greedoids have been studied in relation to the Greedy Algorithm and therefore it is not surprising that these structures are inter-linked in various ways. However, it is quite surprising that the Gauss greedoids and the strong greedoids, approached from quite different points of view, turn out to be precisely the same. Although this can be seen very indirectly by combining the two sets of separate results, the main purpose of this short paper is to prove directly that the two structures are identical, thus giving a simple axiomatic characterisation of the Gauss greedoids. We also note that the transversal greedoids provide an interesting class of examples of such greedoids.