The Quandles with Two Operations / Fedoseev D.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 6. P. 11-15 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
Virtual quandles with two operations and the corresponding invariants of long virtual knots are discussed. A certain knot invariant is constructed and an example of proof that two knots are not equivalent in terms of this invariant is presented.
quandle, distributive grouppoid, biquandle, long virtual knot,
virtual trefoil, colourings invariant.