Surcingle longe lines, requires the use of a surcingle to thread the longe lines through the rings. Compared to a saddle, a surcingle allows more precise adjustment of side reins due to the placement of additional rings. While a saddle only provides one height to attach the rings (the girth buckles), and can be uneven or at the wrong position, a training surcingle places rings at more appropriate locations for ground work. Many surcingle designs allow the side reins to be attached at several different heights along the sides of the horse. When used without a saddle, a surcingle sits just
Matroid girth spark of a matrix. The girth of a binary matroid gives the cardinality of a minimum even set, a subcollection of a family of sets that includes an even number of copies of each set element. Determining the girth of a binary matroid is NP-hard. Additionally, determining the girth of a linear matroid given by a matrix representing the matroid is W[1]-hard when parameterized by the girth or by the rank of the matroid, but fixed-parameter tractable when parameterized by a combination of the rank and the size of the underlying field. For an arbitrary matroid, given by a independence