Horses in warfare of today's English saddle. Both the Scythians and Assyrians used pads with added felt attached with a surcingle or girth around the horse's barrel for increased security and comfort. Xenophon mentioned the use of a padded cloth on cavalry mounts as early as the 4th century BC. The saddle with a solid framework, or "tree", provided a bearing surface to protect the horse from the weight of the rider, but was not widespread until the 2nd century AD. However, it made a critical difference, as horses could carry more weight when distributed across a solid saddle tree. A solid tree,
Matroid girth oracle, it is impossible to find the girth using a subexponential number of matroid queries. Similarly, for a real linear matroid of rank , with elements, described by an oracle that gives the orientation of any -tuple of elements, it requires formula_1 oracle queries to determine the girth. Computations using a girth oracle (an oracle that reports the smallest dependent subset of a given set of elements) have also been considered. Matroid girth In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is