Hilden, Hugh MichaelMontesinos Amilibia, José MaríaTejada Jiménez, Débora MaríaToro Villegas, Margarita María2023-06-202023-06-2020120034-7426https://hdl.handle.net/20.500.14352/43833Using a new way to represent links, that we call a butter y representation, we assign to each 3-bridge link diagram a sequence of six integers,collected as a triple (p=n; q=m; s=l), such that p q s 2, 0 < n p,0 < m q and 0 < l s. For each 3-bridge link there exists an innite number of 3-bridge diagrams, so we dene an order in the set (p=n; q=m; s=l) and assign to each 3-bridge link L the minimum among all the triples that correspond to a 3-butter y of L, and call it the butter y presentation of L. This presentation extends, in a natural way, the well known Schubert classication of 2-bridge links. We obtain necessary and sucient conditions for a triple (p=n; q=m; s=l) to correspond to a 3-butter y and so, to a 3-bridge link diagram. Given a triple (p=n; q=m; s=l) we give an algorithm to draw a canonical 3-bridge diagram of the associated link. We present formulas for a 3-butter y of the mirror image of a link, for the connected sum of two rational knots and for some important families of 3-bridge links. We present the open question: When do the triples (p=n; q=m; s=l) and (p 0 =n0 ; q0 =m0 ; s0 =l0) represent the same 3-bridge link?engjournal articlehttp://www.scm.org.co/aplicaciones/revista/revistas.php?modulo=Revistahttp://www.scm.org.co/restricted access515.162.8Links3-bridge linksBridge presentationLink diagram3-butterflyButterfly presentationGeometria algebraicaAnálisis combinatorioTopología1201.01 Geometría Algebraica1202.05 Análisis Combinatorio1210 Topología